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    Wyświetlanie 1-47 z 47
    Tytuł:
    On oscillatory solutions of certain difference equations
    Autorzy:
    Grzegorczyk, G.
    Werbowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255794.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    difference equations
    oscillation
    Opis:
    Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
    Źródło:
    Opuscula Mathematica; 2006, 26, 2; 317-326
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Reduction and continuation theorems for Brouwer degree and applications to nonlinear difference equations
    Autorzy:
    Mawhin, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255344.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Brouwer degree
    nonlinear difference equations
    Opis:
    The aim of this note is to describe the continuation theorem of [39,40] directly in the context of Brouwer degree, providing in this way a simple frame for multiple applications to nonlinear difference equations, and to show how the corresponding reduction property can be seen as an extension of the well-known reduction formula of Leray and Schauder [24], which is fundamental for their construction of Leray-Schauder's degree in normed vector spaces.
    Źródło:
    Opuscula Mathematica; 2008, 28, 4; 541-560
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solutions of a class of singular linear systems of difference equations. Part 1
    Autorzy:
    Kanan, Asmaa M.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030103.pdf
    Data publikacji:
    2020
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Drazin inverse
    Rank
    Singular difference equations
    Opis:
    We extend results of Campbell, Meyer, Jr. and Rose of applications of the Drazine inverse to linear systems of differential equations with singular constant coefficients to solutions of linear systems of difference equations A x_(n+1)+B x_n= f_n ,n≥0 when A and B are m×m complex matrices and may both singular, under conditions that rank(A)=1 and trace of A is not equal zero. f_n is an arbitrary function in C^m, and x_n∈C^m. We give a new closed form for all solutions of those systems when they are tractable, using the theory of the Drazin inverse, and a matrix K∈C^(m×m).
    Źródło:
    World Scientific News; 2020, 143; 53-66
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the global attractivity and the periodic character of a recursive sequence
    Autorzy:
    Elsayed, E. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/952823.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    stability
    periodic solutions
    boundedness
    difference equations
    Opis:
    In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence [formula], where the parameters a, b, c, d and e are positive real numbers and the initial conditions x-2, x-1 and x0 are positive real numbers.
    Źródło:
    Opuscula Mathematica; 2010, 30, 4; 431-446
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments
    Autorzy:
    Attia, Emad R.
    El-Matary, Bassant M.
    Chatzarakis, George E.
    Powiązania:
    https://bibliotekanauki.pl/articles/29519176.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    oscillation
    difference equations
    non-monotone argument
    Opis:
    In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving lim sup, which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.
    Źródło:
    Opuscula Mathematica; 2022, 42, 6; 769-791
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New aspects for the oscillation of first-order difference equations with deviating arguments
    Autorzy:
    Attia, Emad R.
    El-Matary, Bassant M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2216188.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    difference equations
    oscillation
    non-monotone advanced arguments
    Opis:
    We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.
    Źródło:
    Opuscula Mathematica; 2022, 42, 3; 393-413
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian
    Autorzy:
    Candito, P.
    D'Agui, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255253.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    constant-sign solution
    difference equations
    Neumann problem
    Opis:
    In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete p-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 683-690
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some difference-delay equations arising in a problem of capital deposits
    Autorzy:
    Kwapisz, Marian
    Bartoszewski, Zbigniew
    Powiązania:
    https://bibliotekanauki.pl/articles/748048.pdf
    Data publikacji:
    1996
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Portfolio theory and financial economics
    Difference equations, additive
    Opis:
    .
    Introduction. We consider a real life problem: a. person has made a deposit of D0 dollars in bank B, which calculates interest on this deposit at in=100•in% after each n+l-st quarter and the interest is compounded at the end of each consecutive year since the deposit date, which means that the interest is capitalised yearly. In the case discussed the basic time unit is a quarter but the conversion period - the time interval at the end of which the interest is compounded - is four quarters (for the terminology see [3]). We ask the following question: what is the balance of the person after n time units, i.e. after n quarters? Such a question is important to people planning various sorts of investments or making arrangements with life insurance institutions. We cannot find an answer to this question in available literature. In particular, it is not to be found in recent books devoted to the subject [see 1-6]. We want to find general formulas that would allow us to express this balance by the other given quantities. Such formulas allow us to solve inverse problems consisting in finding the initial deposit Z)q , the interest rate i or the length of the period after which a capital reaches a given level. In this paper we give explicit formulas for the above-mentioned balance. They can be applied to the problems with any number of payments. At the end of this paper we give some examples of application of these formulas to solving the mentioned inverse problems. The obtained formulas make solving such problems easy. A straightforward application of backward recurrence formulas derived from formula (2), although possible, is quite troublesome.ct
    Źródło:
    Mathematica Applicanda; 1996, 25, 39
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Oscillation conditions for difference equations with several variable delays
    Autorzy:
    El-Matary, Bassant M.
    El-Morshedy, Hassan A.
    Benekas, Vasileios
    Stavroulakis, Ioannis P.
    Powiązania:
    https://bibliotekanauki.pl/articles/29519474.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    oscillation
    difference equations
    non-monotone delays
    first order
    Opis:
    A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.
    Źródło:
    Opuscula Mathematica; 2023, 43, 6; 789-801
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution of infinite slab static problem using the finite strip method by difference equations
    Zastosowanie równań różnicowych w rozwiązaniu problemu statyki nieograniczonej tarczy metodą pasm skończonych
    Autorzy:
    Pawlak, Z.
    Rakowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/279420.pdf
    Data publikacji:
    2009
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    finite element method
    finite strips
    difference equations
    plane slab
    Opis:
    An analytical approach to the solution of an infinite slab static problem using the finite strip method is presented. The structure simply supported on its opposite edges is treated as a discrete one. A regular mesh of identical finite strips approximates the continuous structure. This regular slab discretization enables one to derive a fundamental solution for the two-dimensional discrete strip structure in an analytical, closed form. Equilibrium conditions are derived from the finite element method formulation. The set of the infinite number of equilibrium conditions is replaced by one equivalent difference equation. The solution to this equation is the fundamental function, i.e. Green's function for considered slab strip.
    W pracy zaprezentowano analityczne rozwiązanie problemu statyki nieograniczonej tarczy metodą pasm skończonych. Tarcza swobodnie podparta na przeciwległych krawędziach jest rozwiązywana jako układ dyskretny. Ciągła struktura jest aproksymowana regularną siatką składającą się z identycznych pasm skończonych. Regularny podział pozwala na wyprowadzenie funkcji fundamentalnych dla dwuwymiarowego układu dyskretnego w analitycznej, zamkniętej formie. Warunki równowagi zostały wyprowadzone zgodnie ze sformułowaniem metody elementów skończonych. Układ równań równowagi składający się z nieskończonej liczby równań został zastąpiony jednym, równoważnym równaniem różnicowym. Rozwiązanie tego równania jest funkcją fundamentalną dla rozpatrywanej tarczy.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2009, 47, 3; 629-643
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Reconstruction of potential and boundary conditions for second order difference equations
    Autorzy:
    Currie, Sonja
    Love, Anne
    Powiązania:
    https://bibliotekanauki.pl/articles/962820.pdf
    Data publikacji:
    2018
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Difference equations
    inverse problem
    boundary value problems
    potential
    eigenvalues
    Opis:
    Assume the eigenvalues and the weights are given for a difference boundary value problem and that the form of the boundary conditions at the endpoints is known. In particular, it is known whether the endpoints are fixed (i.e. Dirichlet or non-Dirichlet boundary conditions) or whether the endpoints are free to move (i.e. boundary conditions with affine dependence on the eigenparameter). This work illustrates how the potential as well as the exact boundary conditions can be uniquely reconstructed. The procedure is inductive on the number of unit intervals. This paper follows along the lines of S. Currie and A. Love, Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions, \emph{Quaestiones Mathematicae}, 40 (2017), no. 7, 861−877. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in the above reference, an additional spectrum is required more often than was the case in the unique reconstruction of the potential alone.
    Źródło:
    Commentationes Mathematicae; 2018, 58, 1-2; 1-9
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Kneser-type oscillation criteria for second-order half-linear advanced difference equations
    Autorzy:
    Indrajith, N.
    Graef, John R.
    Thandapani, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/2048703.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    second-order difference equations
    advanced argument
    half-linear
    oscillation
    Opis:
    The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.
    Źródło:
    Opuscula Mathematica; 2022, 42, 1; 55-64
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Difference equations with impulses
    Autorzy:
    Danca, Marius
    Feckan, Michal
    Pospisil, Michal
    Powiązania:
    https://bibliotekanauki.pl/articles/255372.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    difference equations
    impulses
    stability
    fixed points
    Li-Yorke chaos
    Opis:
    Difference equations with impulses are studied focussing on the existence of periodic or bounded orbits, asymptotic behavior and chaos. So impulses are used to control the dynamics of the autonomous difference equations. A model of supply and demand is also considered when Li-Yorke chaos is shown among others.
    Źródło:
    Opuscula Mathematica; 2019, 39, 1; 5-22
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the asymptotics of the difference equation with a proportional delay
    Autorzy:
    Kundrat, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255684.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    asymptotics of difference equations
    approximation methods for dynamical systems
    Opis:
    This paper deals with asymptotic properties of a vector difference equation with delayed argument Δxk = Axk +Bx(λk], 0 < λ < 1, k = 0,1,2,..., where A, B are constant matrices and the term [λk] is the integer part of λk. Our aim is to emphasize some resemblances between the asymptotic behaviour of this delay difference equation and its continuous counterpart.
    Źródło:
    Opuscula Mathematica; 2006, 26, 3; 499-506
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the stability of some systems of exponential difference equations
    Autorzy:
    Psarros, N.
    Papaschinopoulos, G.
    Schinas, C.J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255823.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    difference equations
    asymptotic behaviour
    global stability
    centre manifold
    biological dynamics
    Opis:
    In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
    Źródło:
    Opuscula Mathematica; 2018, 38, 1; 95-115
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Polynomial quasisolutions of linear differential-difference equations
    Autorzy:
    Cherepennikov, V. B.
    Ermolaeva, P. G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255903.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    differential-difference equations
    neutral type
    initial-value problem
    polynomial quasisolution
    Opis:
    The paper discusses a linear differential-difference equation of neutral type with linear coefficients, when at the initial time moment t = 0 the value of the desired function x(t) is known. The authors are not familiar with any results which would state the solvability conditions for the given problem in the class of analytical functions. A polynomial of some degree N is introduced into the investigation. Then the term "polynomial quasisolution" (PQ-solution) is understood in the sense of appearance of the residual Δ(t) = O(tN), when this polynomial is substituted into the initial problem. The paper is devoted to finding PQ-solutions for the initial-value problem under analysis.
    Źródło:
    Opuscula Mathematica; 2006, 26, 3; 431-443
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Oscillation criteria for linear difference equations with several variable delays
    Autorzy:
    Benekas, Vasileios
    Garab, Ábel
    Kashkynbayev, Ardak
    Stavroulakis, Ioannis P.
    Powiązania:
    https://bibliotekanauki.pl/articles/2049029.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    oscillation
    difference equations
    several delays
    non-monotone argument
    slowly varying function
    Opis:
    We obtain new sufficient criteria for the oscillation of all solutions of linear delay difference equations with several (variable) finite delays. Our results relax numerous well-known limes inferior-type oscillation criteria from the literature by letting the limes inferior be replaced by the limes superior under some additional assumptions related to slow variation. On the other hand, our findings generalize an oscillation criterion recently given for the case of a constant, single delay.
    Źródło:
    Opuscula Mathematica; 2021, 41, 5; 613-627
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences
    Autorzy:
    Schmeidel, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255806.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    linear
    nonlinear
    difference equations
    third order
    oscillatory solution
    quasidifferences
    Riccati technique
    Opis:
    In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.
    Źródło:
    Opuscula Mathematica; 2006, 26, 2; 361-369
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak heteroclinic solutions and competition phenomena to anisotropic difference equations with variable exponents
    Autorzy:
    Guiro, A.
    Kone, B.
    Ouaro, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/952771.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    anisotropic difference equations
    heteroclinic solutions
    discrete Hölder type inequality
    competition phenomena
    Opis:
    In this paper, we prove the existence of weak heteroclinic solutions for a family of anisotropic difference equations under competition phenomena between parameters.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 733-745
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Global attractivity of a higher order nonlinear difference equation with unimodal terms
    Autorzy:
    Almaslokh, Abdulaziz
    Qian, Chuanxi
    Powiązania:
    https://bibliotekanauki.pl/articles/29519331.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    higher order difference equations
    positive equilibrium
    unimodal term
    global attractivity
    population model
    Opis:
    In the present paper, we study the asymptotic behavior of the following higher order nonlinear difference equation with unimodal terms x(n + 1) = ax(n) + bx(n)g(x(n)) + cx(n − k)g(x(n − k)), n = 0, 1, . . . , where a, b and c are constants with 0 < a < 1, 0 ≤ b < 1, 0 ≤ c < 1 and a + b + c = 1, g ∈ C[[0,∞), [0,∞)] is decreasing, and k is a positive integer. We obtain some new sufficient conditions for the global attractivity of positive solutions of the equation. Applications to some population models are also given.
    Źródło:
    Opuscula Mathematica; 2023, 43, 2; 131-143
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities
    Autorzy:
    Chidouh, A.
    Torres, D. F. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255913.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional difference equations
    Lyapunov-type inequalities
    fractional boundary value problems
    positive solutions
    Opis:
    We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
    Źródło:
    Opuscula Mathematica; 2018, 38, 1; 31-40
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A boundary value problem for a non-linear difference equation
    Autorzy:
    Lefebvre, Mario
    Powiązania:
    https://bibliotekanauki.pl/articles/27324014.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    higher-order difference equations
    optimal control
    dynamic programming
    first-passage time
    homing problem
    Opis:
    A boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear difference equation that can be used to find an explicit solution to this equation. An example is presented.
    Źródło:
    Archives of Control Sciences; 2023, 33, 4; 829--837
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On criteria for algebraic independence of collections of functions satisfying algebraic difference relations
    Autorzy:
    Ogawara, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/255709.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    difference algebra
    systems of algebraic difference equations
    algebraic independence
    Vignéras’multiple gamma functions
    q-polylogarithm functions
    Opis:
    This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1) Vignéras’ multiple gamma functions and derivatives of the gamma function, (2) the logarithmic function, q-exponential functions and q-polylogarithm functions. In a similar way, we give a generalization of Ostrowski’s theorem.
    Źródło:
    Opuscula Mathematica; 2017, 37, 3; 457-472
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some stability conditions for scalar Volterra difference equations
    Autorzy:
    Berezansky, L.
    Migda, M.
    Schmeidel, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/254995.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    linear and nonlinear Volterra difference equations
    boundedness of solutions
    exponential and asymptotic stability
    Opis:
    New explicit stability results are obtained for the following scalar linear difference equation [formula] and for some nonlinear Volterra difference equations.
    Źródło:
    Opuscula Mathematica; 2016, 36, 4; 459-470
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of three solutions for perturbed nonlinear difference equations
    Autorzy:
    Heidarkhani, S.
    Moghadam, M. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/952774.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonlinear difference equations
    discrete boundary value problem
    three solutions
    critical point theory
    variational methods
    Opis:
    Using critical point theory, we study the existence of at least three solutions for perturbed nonlinear difference equations with discrete boundary-value condition depending on two positive parameters.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 747-761
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Difference scheme for differential-difference problems with small shifts arising in computational model of neuronal variability
    Autorzy:
    Kodipaka, Mamatha
    Emineni, Siva Prasad
    Kolloju, Phaneendra
    Powiązania:
    https://bibliotekanauki.pl/articles/2174179.pdf
    Data publikacji:
    2022
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    siatka niejednorodna
    równanie różniczkowe
    warstwa brzegowa
    non-uniform grid
    differential-difference equations
    boundary layer
    Opis:
    The solution of differential-difference equations with small shifts having layer behaviour is the subject of this study. A difference scheme is proposed to solve this equation using a non-uniform grid. With the non-uniform grid, finite - difference estimates are derived for the first and second-order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the tridiagonal system algorithm. Convergence of the scheme is examined. Various numerical simulations are presented to demonstrate the validity of the scheme. In contrast to other techniques, maximum errors in the solution are organized to support the method. The layer behaviour in the solutions of the examples is depicted in graphs.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2022, 27, 1; 91--106
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The numerical solution of functional differential equations, a survey
    Autorzy:
    Jackiewicz, Z.
    Kwapisz, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/748493.pdf
    Data publikacji:
    1991
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Difference and functional equations, recurrence relations
    Neutral equations
    Opis:
    .
    Significant progress has been made in the last few years in the numerical solution of functional differential equations. It is the purpose of this paper to review the results in this area. Special attention is given to implementation of one-step methods and predictor corrector methods for functional differential equations including equations of neutral type and to the stability theory of numerical methods for these equations.
    Źródło:
    Mathematica Applicanda; 1991, 19, 33
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Oscillation of second order difference equation with a sub-linear neutral term
    Autorzy:
    Dharuman, C.
    Graef, J. R.
    Thandapani, E.
    Vidhyaa, K. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/357828.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    difference equations
    oscillation
    second orde
    sub-linear neutral term
    równania różniczkowe
    oscylacja
    równania drugiego rzędu
    Opis:
    This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.
    Źródło:
    Journal of Mathematics and Applications; 2017, 40; 59-67
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sustainable Exploitation of Biological Populations
    Autorzy:
    Grasman, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/929749.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    rybołówstwo
    równanie różnicowe
    optimal harvesting
    system of nonlinear difference equations
    fishery
    host-parasitoid system
    stabilizing feedback
    Opis:
    For a system of nonlinear difference equations that models the dynamics of exploited biological populations, a locally optimal periodic solutionis constructed. If this solution is unstable, a stabilizing feedback in the harvesting is introduced. The method is applied to an age-structured population model in fishery as well as to a host-parasitoid system for which the number of hosts and the number of introduced parasitoids shouldbe minimized.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2000, 10, 1; 123-129
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dynamic system with random structure for modeling security and risk management in cyberspace
    Autorzy:
    Dzhalladova, Irada
    Ruzickova, Miroslava
    Powiązania:
    https://bibliotekanauki.pl/articles/952816.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    semi-Markov chain
    random transformation of solutions the Lyapunov function
    instability
    systems of difference equations
    jumps of solutions
    cybersecurity
    Opis:
    We deal with the investigation of L2-stability of the trivial solution to the system of difference equations with coefficients depending on a semi-Markov chain. In our considerations, random transformations of solutions are assumed. Necessary and sufficient conditions for L2-stability of the trivial solution to such systems are obtained. A method is proposed for constructing Lyapunov functions and the conditions for its existence are justified. The dynamic system and methods discussed in the paper are very well suited for use as models for protecting information in cyberspace.
    Źródło:
    Opuscula Mathematica; 2019, 39, 1; 23-37
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Eigenvalue-eigenfunction problem for Steklovs smoothing operator and differential-difference equations of mixed type
    Autorzy:
    Iakovlev, S. I.
    Iakovleva, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/254795.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Steklov's smoothing operator
    spectrum
    eigenvalues
    eigenfunctions
    mixed-type differential-difference equations
    initial function
    method of steps
    countably normed space
    transformation group
    generator
    Opis:
    It is shown that any μ ∈ C is an infinite multiplicity eigenvalue of the Steklov smoothing operator Sh acting on the space [formula]. For μ ≠ 0 the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theorem is proved for this equation. Further a transformation group is defined on a countably normed space of initial functions and the spectrum of the generator of this group is studied. Some possible generalizations are pointed out.
    Źródło:
    Opuscula Mathematica; 2013, 33, 1; 81-98
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Binomial ARMA count series from renewal processes
    Autorzy:
    Koshkin, Sergiy
    Cui, Yunwei
    Powiązania:
    https://bibliotekanauki.pl/articles/729904.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    integer-valued time series
    stochastic difference equations
    autoregressive moving average
    renewal process
    lifetime distribution
    probability generating function
    palindromic polynomial
    constant hazard rate
    Opis:
    This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p,p-1) series from lifetime distributions with constant hazard rates after lag p are given as an illustration.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2012, 32, 1-2; 5-16
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    q-analogue of summability of formal solutions of some linear q-difference-differential equations
    Autorzy:
    Tahara, H.
    Yamazawa, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/1397578.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    q-difference-differential equations
    summability
    formal power series solutions
    q-Gevrey asymptotic expansions
    q-Laplace transform
    Opis:
    Let q > 1. The paper considers a linear q-difference-differential equation: it is a q-difference equation in the time variable t, and a partial differential equation in the space variable z. Under suitable conditions and by using q-Borel and q-Laplace transforms (introduced by J.-P. Ramis and C. Zhang), the authors show that if it has a formal power series solution X(t, z) one can construct an actual holomorphic solution which admits X(t, z) as a q-Gevrey asymptotic expansion of order 1.
    Źródło:
    Opuscula Mathematica; 2015, 35, 5; 713-738
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Implicit difference methods for infinite systems of hyperbolic functional differential equations
    Autorzy:
    Szafrańska, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/745990.pdf
    Data publikacji:
    2010
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    initial boundary value problems
    difference functional equations
    difference methods
    stability and convergence
    interpolating operators
    nonlinear estimates of the Perron type
    Opis:
    The paper deal with classical solutions of initial boundary value problems for infinite systems of nonlinear differential functional equations. Two types of difference schemes are constructed. First we show that solutions of our differential problem can be approximated by solutions of infinite difference functional schemes. In the second part of the paper we proof that solutions of finite difference systems approximate the solutions of aur differential problem. We give a complete convergence analysis for both types of difference methods. We adopt nonlinear estimates of the Perron type for given functions with respect to the functional variable. The proof of the stability is based on the comparison technique. Numerical examples are presented.
    Źródło:
    Commentationes Mathematicae; 2010, 50, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonstationary analysis of the queueing network with bypass of systems of multi-type and absolute priority messages
    Autorzy:
    Matalytski, M.
    Naumenko, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/122976.pdf
    Data publikacji:
    2013
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    multi-type messages bypass of systems
    absolute priority
    conditional probabilities of transitions
    system of difference-differential equations
    probability states
    generating function
    Opis:
    This paper contains an investigation of an open exponential network with bypass of systems of multi-type messages with absolute priority in transient behavior. Messages with priority received by the node with the probability depending on the state system and the type of incoming messages are for service, forcing messages that are serviced or instant changes in the following system, and can leave the network. Network settings: the intensity of the incoming flow and the intensity of service of different types of messages in single-line systems and the conditional probabilities of transitions of messages between the systems are dependent on the time. We obtained a system difference-differential equations for the state probabilities of the network. To find the state probabilities of the network in the transitional behavior applied a methodology based on the use of the apparatus of multidimensional generating functions.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 1; 93-105
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some classes of Diophantine equations connected with McFarland's and Ma's conjectures
    Autorzy:
    Cao, Zhenfu
    Grytczuk, Aleksander
    Powiązania:
    https://bibliotekanauki.pl/articles/728804.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    difference sets
    diophantine equations
    Pell's equations
    Opis:
    In this paper we consider some special classes of Diophantine equations connected with McFarland's and Ma's conjectures about difference sets in abelian groups and we obtain an extension of known results.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 193-198
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonstationary analysis of a queueing network with positive and negative messages
    Autorzy:
    Matalytski, M.
    Naumenko, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/122613.pdf
    Data publikacji:
    2013
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    information systems
    telecommunications systems
    information networks
    telecommunications networks
    virus
    open G-network with negative messages
    transient behavior
    system of difference-differential equations
    probability states
    generating function
    Opis:
    This paper contains an investigation of an open queueing network with positive and negative messages that can be used to model the behavior of viruses in information and telecommunication systems and networks. The purpose of research is investigation of such a network at the transient behavior. We consider the case when the intensity of the incoming flow of positive and negative messages and service intensity of messages do not depend on time. It is assumed that all queueing systems of network are one-line. We obtained a system difference-differential equations for the state probabilities of the network. To find the state probabilities of the network in the transitional behavior applied a methodology based on the use of the apparatus of multidimensional generating functions. We obtained an expression for generating function. An example is calculated.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 2; 61-71
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Critical cases in neutral functional differential equations, arising from hydraulic engineering
    Autorzy:
    Răsvan, Vladimir
    Powiązania:
    https://bibliotekanauki.pl/articles/2216162.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    1D hyperbolic partial differential equations
    neutral functional differential equation
    difference operator
    critical case
    differential equations
    Opis:
    This paper starts from several applications described by initial/boundary value problems for 1D (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties.
    Źródło:
    Opuscula Mathematica; 2022, 42, 4; 605-633
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Estimates of solutions for parabolic differential and difference functional equations and applications
    Autorzy:
    Sapa, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/254895.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    parabolic differential and discrete functional equations
    estimate of solution
    implicit difference method
    Opis:
    The theorems on the estimates of solutions for nonlinear second-order partial differential functional equations of parabolic type with Dirichlet's condition and for suitable implicit finite difference functional schemes are proved. The proofs are based on the comparison technique. The convergent and stable difference method is considered without the assumption of the global generalized Perron condition posed on the functional variable but with the local one only. It is a consequence of our estimates theorems. In particular, these results cover quasi-linear equations. However, such equations are also treated separately. The functional dependence is of the Volterra type.
    Źródło:
    Opuscula Mathematica; 2012, 32, 3; 529-549
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Neumann’s condition
    Autorzy:
    Sapa, Lucjan
    Powiązania:
    https://bibliotekanauki.pl/articles/962640.pdf
    Data publikacji:
    2009
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    parabolic differential functional equations
    difference methods
    nonlinear estimates of the generalized Perron type
    Opis:
    Classical solutions of nonlinear second-order partial differential functional equations of parabolic type with Neumann’s condition are approximated in the paper by solutions of associated explicit difference functional equations. The functional dependence is of the Volterra type. Nonlinear estimates of the generalized Perron type for given functions are assumed. The convergence and stability results are proved with the use of the comparison technique. These theorems in particular cover quasi-linear equations, but such equations are also treated separately. The known results on similar difference methods can be obtained as particular cases of our simple result.
    Źródło:
    Commentationes Mathematicae; 2009, 49, 1; 83-106
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Investigation of the Stability and Convergence of Difference Schemes for the Three-dimensional Equations of the Atmospheric Boundary Layer
    Autorzy:
    Temirbekov, A. N.
    Urmashev, B. A.
    Gromaszek, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/226826.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    atmospheric boundary layer equations
    difference scheme
    approximation error
    stability
    convergence algorithms
    numerical solution
    Opis:
    In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved.
    Źródło:
    International Journal of Electronics and Telecommunications; 2018, 64, 3; 391-396
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical study on two dimensional distribution of streamwise velocity in open channel turbulent flows with secondary current effect
    Autorzy:
    Mohan, S.
    Kundu, S.
    Ghoshal, K.
    Kumar, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/38616700.pdf
    Data publikacji:
    2021
    Wydawca:
    Instytut Podstawowych Problemów Techniki PAN
    Tematy:
    velocity distribution
    open channel flow
    turbulent flow
    RANS equations
    secondary current
    finite difference method
    Opis:
    For studying mechanism of sediment transport in river flows, open channel flow is a prototype. Flow has always three components of velocity for all types of channel geometry and for a time independent uniform flow along streamwise or main flow direction, all the components of velocity are functions of lateral and vertical coordinates. The present study investigates the two dimensional distribution of streamwise (or longitudinal) velocity starting from the Reynolds averaged Navier–Stokes equation for a turbulent open channel flow which is steady and uniform along the main flow direction. Secondary flows both along the vertically upward direction and along the lateral direction are considered which are also taken as functions of lateral and vertical coordinates. Inclusion of the secondary current brings the effect of dip phenomenon in the model. The resulting second order partial differential equation is solved numerically. The model is validated for all the cross-sectional, transverse and centreline velocity distribution by comparing with existing relevant set of experimental data and also with an existing model. Comparison results show good agreement with data as well as with the previous model proving the efficiency of the model. It is found that the transverse velocity distribution depends on the formation of circular vortex in the cross-sectional plane and becomes periodic as the number of circular vortex increases for increasing aspect ratios.
    Źródło:
    Archives of Mechanics; 2021, 73, 2; 175-200
    0373-2029
    Pojawia się w:
    Archives of Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Difference methods for infinite systems of hyperbolic functional differential equations on the Haar pyramid
    Autorzy:
    Jaruszewska-Walczak, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/2050179.pdf
    Data publikacji:
    2004
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    initial problems
    infinite systems of differential functional equations
    difference functional inequalities
    nonlinear estimates of Perron type
    Opis:
    We consider the Cauchy problem for infinite system of differential functional equations $\partial_{t}z_{k}(t, x) = f_{k}(t, x, z, \partial_{x}z_{k}(t, x)), k \in \mathbf{N}$. In the paper we consider a general class of difference methods for this problem. We prove the convergence of methods under the assumptions that given functions satisfy the nonlinear estimates of the Perron type with respect to functional variables. The proof is based on functional difference inequalities. We constructed the Euler method as an example of difference method.
    Źródło:
    Opuscula Mathematica; 2004, 24, 1; 85-96
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Numerical solution for the problem of heat and mass flow in the soil heated with warm air
    Autorzy:
    Bożek, B.
    Kurpaska, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/241006.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
    Tematy:
    numerical solution
    heat flow
    mass flow
    soils
    warm air
    differential equations
    greenhouse substrate
    system of heating pipes
    explicite-implicite difference scheme
    Opis:
    In this paper a difference method of solving the system of differential equations is presented for differential equations, describing the distribution of temperature and water content in the greenhouse substrate heated with a system of heating pipes. The algorithm of solving the proposed method (explicite-implicite difference scheme) is presented. In addition, the effects of temperature and water content changes obtained from the solution of proposed the model as well as the model where the thermal diffusion of mass was included were compared.
    Źródło:
    Archives of Hydro-Engineering and Environmental Mechanics; 2000, 47, 1-4; 75-96
    1231-3726
    Pojawia się w:
    Archives of Hydro-Engineering and Environmental Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modeling of heat transfer and fluid flow in a rectangular channel with an obstacle
    Autorzy:
    Stryczyński, Mikołaj
    Majchrzak, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/1839780.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    channel with an obstacle
    Fourier-Kirchhoff equation
    Navier-Stokes equations
    finite difference method
    równanie Fouriera-Kirchhoffa
    równania Naviera-Stokesa
    metoda różnic skończonych
    Opis:
    Heat transfer and fluid flow in the rectangular channel with an obstacle are considered. The problem is described by the Fourier-Kirchhoff equation, Navier-Stokes equations and continuity equation supplemented by appropriate boundary and initial conditions. To solve this system of equations the finite difference method with a staggered grid is used. The results of computations obtained using authorial computer program are compared with ANSYS Fluent simulation. Computations are carried out for obstacles of various sizes and positions, and on this basis the conclusions are formulated.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 2; 121-132
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term
    Autorzy:
    Błasik, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/2086846.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional derivative
    fractional integral
    integro-differential equations
    numerical method
    finite difference method
    pochodna ułamkowa
    całkowanie ułamkowe
    równanie całkowo-różniczkowe
    metoda numeryczna
    metoda elementów skończonych
    Opis:
    In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 6; e138240, 1--9
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical simulation of channel flow over a skewed equilateral cavity
    Autorzy:
    Kamel, Abanoub G.
    Haraz, Eman H.
    Hanna, Sarwat N.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839759.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    finite difference method
    incompressible flow
    channel flow
    lid-driven
    shear-driven
    skewed cavity
    Navier-Stokes equations
    równanie Naviera-Stokesa
    przepływ nieściśliwy
    metoda różnic skończonych
    przepływ kanałowy
    Opis:
    In this paper, an incompressible, two-dimensional (2D), time-dependent, Newtonian, laminar, and internal channel fluid flow over a skewed equilateral cavity is simulated using the finite difference method (FDM) and alternating direction implicit (ADI) technique. Navier-Stokes equations are solved numerically in stream function-vorticity formulation. The goal of tackling this problem depends on its academic significance by studying the difference between lid-driven and shear-driven cavity flows in terms of the formation of Moffatt eddies at the sharp corner, also to obtain the length and intensity ratios of these counter-rotating vortices. The value of velocity components along the centerlines of the skewed cavity was revealed at low and intermediate Reynolds numbers (Re), typically (Re = 200 and 2000) at two different skew angles of mainly 30° and 45°. Likewise, the blocked-off regions’ method is used to deal with the geometry of the skewed cavity especially the sharp corners. Furthermore, as Re increases, the main vortex approaches the skewed cavity center and the counter-rotating vortices get bigger in size and intensity, and their number increases.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 3; 29-43
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-47 z 47

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