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Wyświetlanie 1-15 z 132
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:
A difference scheme for an elliptic system of nonlinear differential-functional equations with Dirichlet type boundary conditions. The existence and uniqueness of solution
Autorzy:
Bożek, Bogusław
Mosurski, Ryszard
Powiązania:
https://bibliotekanauki.pl/articles/715036.pdf
Data publikacji:
1984
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Źródło:
Annales Polonici Mathematici; 1984, 44, 2; 155-161
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
Autorzy:
Malec, M.
Sapa, L.
Powiązania:
https://bibliotekanauki.pl/articles/255499.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
partial differential equation
parabolic-elliptic system
finite difference method
finite difference scheme
consistence
convergence
stability
error estimate
uniqueness
Opis:
This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in R1+n. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
Źródło:
Opuscula Mathematica; 2007, 27, 2; 259-289
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:
A numerical solution for a class of time fractional diffusion equations with delay
Autorzy:
Pimenov, V. G.
Hendy, A. S.
Powiązania:
https://bibliotekanauki.pl/articles/330624.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional diffusion equation
difference scheme
convergence analysis
równanie dyfuzji ułamkowe
schemat różnicowy
analiza zbieżności
Opis:
This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ 2−α + h4) in L ∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 477-488
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A robust computational technique for a system of singularly perturbed reaction–diffusion equations
Autorzy:
Kumar, V.
Bawa, R. K.
Lal, A. K.
Powiązania:
https://bibliotekanauki.pl/articles/330202.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
asymptotic expansion approximation
backward difference operator
trapezoidal method
piecewise uniform Shishkin mesh
rozwinięcie asymptotyczne
operator różnicowy
metoda trapezowa
Opis:
In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 387-395
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic behavior of solutions of discrete Volterra equations
Autorzy:
Migda, J
Migda, M.
Powiązania:
https://bibliotekanauki.pl/articles/254889.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Volterra difference equation
prescribed asymptotic behaviour
asymptotically polynomial solution
asymptotically periodic solution
bounded solution
Opis:
We consider the nonlinear discrete Volterra equations of non-convolution type [formula] We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, especially asymptotically polynomial and asymptotically periodic solutions. We use o(ns), for a given nonpositive real s, as a measure of approximation. We also give conditions under which all solutions are asymptotically polynomial.
Źródło:
Opuscula Mathematica; 2016, 36, 2; 265-278
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic behaviour of solutions of difference equations in Banach spaces
Autorzy:
Kisiołek, Anna
Powiązania:
https://bibliotekanauki.pl/articles/729477.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Banach space
difference equation
fixed point
measure of noncompactness
asymptotic behaviour of solutions
Opis:
In this paper we consider the first order difference equation in a Banach space
$Δx_{n} = ∑_{i=0}^∞ a^{i}_{n} f(x_{n+i})$.
We show that this equation has a solution asymptotically equal to a.
As an application of our result we study the difference equation
$Δx_{n} = ∑_{i=0}^∞ a^i_{n}g(x_{n+i}) + ∑_{i=0}^∞ b^{i}_{n}h(x_{n+i}) + y_{n}$
and give conditions when this equation has solutions.
In this note we extend the results from [8,9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 5-13
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations
Autorzy:
Migda, M.
Powiązania:
https://bibliotekanauki.pl/articles/255688.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
neutral difference equation
asymptotic behavior
nonoscillatory solution
Opis:
In this paper we study asymptotic behavior of solutions of a higher order neutral difference equation of the form Δm(xn + pnxn-τ) + f(n, xσ(n)) = hn. We present conditions under which all nonoscillatory solutions of the above equation have the property xn = cnm-1 + o(nm-1) for some c ∈ R.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 507-514
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:
Comparison of bio-heat transfer numerical models based on the Pennes and Cattaneo-Vernotte equations
Autorzy:
Ciesielski, M.
Duda, M.
Mochnacki, B.
Powiązania:
https://bibliotekanauki.pl/articles/122908.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
bioheat transfer
Pennes equation
Cattaneo-Vernotte equation
numerical modeling of heating process
finite difference method
przepływ biociepła
równanie Pennesa
równanie Cattaneo-Vernotte
metoda różnic skończonych
modelowanie numeryczne
Opis:
The homogeneous soft tissue domain subjected to an external heat source is considered. Thermal processes in this domain are described using the well known Pennes equation and next the Cattaneo-Vernotte one. Within recent years the prevailing view is that the Cattaneo-Vernotte equation better describes the thermal processes proceeding in the biological tissue (it results from the specific internal tissue structure). Appearing in this equation the delay time of heat flux with respect to the temperature gradient (τq) is of the order of several seconds and the different values of τq are taken into account. At the stage of numerical modeling the finite difference method is used. In the final part of the paper, the examples of computations are shown.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 4; 33-38
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 132

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