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Wyświetlanie 1-15 z 53
Tytuł:
Asymptotic of weak solutions for linear elliptic nonlocal Robin problem without Dini-continuity condition in a plane angle domain
Autorzy:
Żyjewski, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/960139.pdf
Data publikacji:
2017
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
boundary value problems
weak solutions
second order elliptic linear equations
nonlocal Robin problem
corner points
Dini-continuity
Opis:
We investigate the behaviour of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighbourhood of the boundary corner point. We find the exponent of the solution decreasing rate under the assumption that the leading coefficients of the equations do not satisfy the Dini-continuity condition.
Źródło:
Commentationes Mathematicae; 2017, 57, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Initial boundary value problems for vortex motion of an ideal fluid in bounded domains
Autorzy:
Szmidt, K.
Powiązania:
https://bibliotekanauki.pl/articles/241010.pdf
Data publikacji:
2001
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
vortex motion
incompressible perfect fluid
bounded domains
boundary value problems
water wave
Opis:
The paper deals with the problem of vortex motion of an incompressible perfect fluid in bounded domains. The research is confined to chosen cases of steady velocity fields within rectangular, circular and elliptic regions with rigid boundaries. The solution to the initial-value problem of the fluid flow for the assumed velocity fields is the primary object of this paper. It is demonstrated that individual particles of the fluid have their own periods of motion and thus, one should be careful in describing such problems by means of discrete methods, especially in the Lagrangian variables. The problem discussed has its origin in numerical analysis of water waves by means of the finite difference or the finite element method.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2001, 48, 1; 19-33
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
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:
Weighted difference schemes for systems of quasilinear first order partial functional differential equations
Autorzy:
Szafrańska, Anna
Powiązania:
https://bibliotekanauki.pl/articles/747972.pdf
Data publikacji:
2015
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
initial boundary value problems, difference methods, stability and convergence, interpolating operators, error estimates, comparison methods
zagadnienia początkowo-brzegowe, metody różnicowe, stabilność i zbieżność, operatory interpolacyjne, oszacowanie błędu, metody porównawcze.
Opis:
Praca dotyczy zagadnien poczatkowo brzegowych typu Dirichlet’a dlaukładów quasiliniowych równan rózniczkowo-funkcyjnych. Zamieszczona jest konstrukcjawazonych metod róznicowych dla wyjsciowych zagadnien rózniczkowychoraz przeprowadzona jest pełna analiza zbieznosci. Niezbedne załozenia obejmujaoszacowania typu Perrona dla funkcji danych wzgledem argumentów funkcyjnych.Dowód stabilnosci metody róznicowej opiera sie na technice porównawczej. Teoretycznerezultaty zobrazowane sa na przykładzie całkowego równania rózniczkowegooraz równan rózniczkowych z odchylonym argumentem.
The paper deals with initial boundary value problems of the Dirichlet type for system of quasilinear functional differential equations.We investigate weighted difference methods for these problems.A complete convergence analysis of the considered difference methods is given. Nonlinear estimates of the Perron type with respect to functional variables for given functions are assumed. The proof of the stability of difference problems is based on a comparison technique. The results obtained here can be applied to differential integral problems and differential equations with deviated variables.Numerical examples are presented.
Źródło:
Mathematica Applicanda; 2015, 43, 2
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Difference functional inequalities and applications
Autorzy:
Szafrańska, A.
Powiązania:
https://bibliotekanauki.pl/articles/255602.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
initial boundary value problems
difference functional inequalities
difference methods
stability and convergence
interpolating operators
error estimates
Opis:
The paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 405-423
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian
Autorzy:
Smejda, J.
Wieteska, R.
Powiązania:
https://bibliotekanauki.pl/articles/952772.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
discrete boundary value problems
variational methods
mountain pass theorem
Opis:
In this paper we study the existence and the nonexistence of solutions for the boundary value problems of a class of nonlinear second-order discrete equations depending on a parameter. Variational (the mountain pass technique) and non-variational methods are applied.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 851-870
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Lebesgue and Sobolev spaces on a time-scale
Autorzy:
Skrzypek, Ewa
Szymańska-Dębowska, Katarzyna
Powiązania:
https://bibliotekanauki.pl/articles/255732.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Lebesgue spaces
Sobolev spaces
modular spaces
time-scales
boundary value problems on time-scales
Opis:
We consider the generalized Lebesgue and Sobolev spaces on a bounded time-scale. We study the standard properties of these spaces and compare them to the classical known results for the Lebesgue and Sobolev spaces on a bounded interval. These results provide the necessary framework for the study of boundary value problems on bounded time-scales.
Źródło:
Opuscula Mathematica; 2019, 39, 5; 705-731
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An analysis of the exterior Neumann problem for the Poisson equation in connection with a numerical procedure
Autorzy:
Roliński, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/747373.pdf
Data publikacji:
1993
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Boundary element methods
Boundary value problems for second-order elliptic equations
Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Opis:
.
This paper is concerned with transforming the exterior problem Δu=f on Ωc, (∂u/∂n)|Γ=g, where ΩR2 is a bounded region and Ω^(c)=int(R2\Ω), into a problem represented by two equations. The first one is posed on a bounded domain and the second one is posed on the outer part of the boundary of the domain. This new problem is suitable for a numerical method based on coupling the finite and boundary element methods.
Źródło:
Mathematica Applicanda; 1993, 22, 36
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Methods of solving operator eigenproblems in parallel distributed memory systems as applied in electromagnetics
Autorzy:
Rewieński, M.
Powiązania:
https://bibliotekanauki.pl/articles/1953952.pdf
Data publikacji:
1998
Wydawca:
Politechnika Gdańska
Tematy:
operator eigenproblems
parallel numerical methods
computational electromagnetics
boundary value problems
Opis:
This study presents numerical methods of solving operator eigenproblems, focusing on their applications in electromagnetics. The discussion concentrates on the analysis of new iterative algorithms or modifications of the existing ones, which are capable of finding a few eigenvalues from the point spectrum of a non-symmetric operator. The salient feature of the considered methods is a low computational cost and memory complexity as compared to alternative solutions. This paper also presents implementations of the investigated algorithms in parallel distributed memory systems, based on the message-passing parallel programming model and providing portable parallel eigensolvers. The discussion of the applied designs of the parallel algorithms is supported by the presentation of the results of performance tests in selected distributed memory environments, including scalable parallel supercomputer systems and networks of workstations. The results of these tests confirm high efficiency of the eigensolvers in the considered parallel environments. In this study attention is also drawn to the question of the applicability of the eigensolvers to problems of modelling of electromagnetic fields in dielectric waveguides. The results of numerical tests validating the methods in these applications determine the scope of problems which may be most effectively solved using the specific eigensolvers.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 1998, 2, 4; 611-731
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation of eigenvalues of nonselfadjoint problems on an infinite interval
Autorzy:
Regińska, Teresa
Powiązania:
https://bibliotekanauki.pl/articles/748435.pdf
Data publikacji:
1979
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Linear boundary value problems,Linear equations,Eigenvalue problems
Opis:
W pracy badane są zagadnienia własne Lu=a u. Dowodzi się, iż wartości własne tego zagadnienia są aproksymowane przez wartości własne pewnych zagadnień własnych na przedziałach skończonych.
The author treats the problem of approximation of the eigenvalues of the nonselfadjoint problem Lu=λu, u(0)=0, u∈L2(0,∞), where L=−d2/dt2+p(x), domL={u∈L2(0,∞):du/dt continuous, d2u/dt2∈L2(0,∞), u(0)=0}. The same question for a selfadjoint problem was answered in the author's recent paper.
Źródło:
Mathematica Applicanda; 1979, 7, 14
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Superconvergence effect in finite element methods for two-point boundary value problems
Autorzy:
Regińska, Teresa
Powiązania:
https://bibliotekanauki.pl/articles/747715.pdf
Data publikacji:
1987
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Boundary value problems
Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
Opis:
.
Approximate methods for solving two-point boundary value problems are considered. The aim of the paper is to explain superconvergence effect in the methods using finite element spaces. The existence of a class of the methods with the superconvergence property is demonstrated. Detailed proofs of superconvergence are presented for the case of the Galerkin method (due to Douglas and Dupont results) and for some example of external method.
Źródło:
Mathematica Applicanda; 1987, 16, 30
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions
Autorzy:
R., D.
Wang, Haiyan
Powiązania:
https://bibliotekanauki.pl/articles/1294312.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear boundary value problems
multiplicity of positive solutions
upper and lower solutions
degree theory
Opis:
We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.
Źródło:
Annales Polonici Mathematici; 1998, 69, 2; 155-165
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On solutions of integral equations with analytic kernels and rotations
Autorzy:
Nguyen, Mau
Nguyen, Tuan
Powiązania:
https://bibliotekanauki.pl/articles/1311183.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
integral operators
singular integral equations
algebraic operators
Riemann boundary value problems
Opis:
We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*)     x(t) + a(t)(Tx)(t) = b(t), where $T = M_{n₁,k₁} ... M_{n_m,k_m}$ and $M_{n_j,k_j}$ are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial $P_T(t) = t³ - t$. By means of the Riemann boundary value problems, we give an algebraic method to obtain all solutions of equation (*) in closed form.
Źródło:
Annales Polonici Mathematici; 1996, 63, 3; 293-300
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of linear and non-linear boundary value problems using population-distributed parallel differential evolution
Autorzy:
Nasim, Amnah
Burattini, Laura
Fateh, Muhammad Faisal
Zameer, Aneela
Powiązania:
https://bibliotekanauki.pl/articles/91569.pdf
Data publikacji:
2019
Wydawca:
Społeczna Akademia Nauk w Łodzi. Polskie Towarzystwo Sieci Neuronowych
Tematy:
parallel evolutionary algorithms
differential evolution
boundary value problems
optimization
Opis:
Cases where the derivative of a boundary value problem does not exist or is constantly changing, traditional derivative can easily get stuck in the local optima or does not factually represent a constantly changing solution. Hence the need for evolutionary algorithms becomes evident. However, evolutionary algorithms are compute-intensive since they scan the entire solution space for an optimal solution. Larger populations and smaller step sizes allow for improved quality solution but results in an increase in the complexity of the optimization process. In this research a population-distributed implementation for differential evolution algorithm is presented for solving systems of 2nd-order, 2-point boundary value problems (BVPs). In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraint boundary conditions and is then solved using differential evolution in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. Four benchmark BVPs are solved using the proposed parallel framework for differential evolution to observe the speedup in the execution time. Meanwhile, the statistical analysis is provided to discover the effect of parametric changes such as an increase in population individuals and nodes representing features on the quality and behavior of the solutions found by differential evolution. The numerical results demonstrate that the algorithm is quite accurate and efficient for solving 2nd-order, 2-point BVPs.
Źródło:
Journal of Artificial Intelligence and Soft Computing Research; 2019, 9, 3; 205-218
2083-2567
2449-6499
Pojawia się w:
Journal of Artificial Intelligence and Soft Computing Research
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Riemann problem on the double of a multiply connected circular region
Autorzy:
Mityushev, V.
Powiązania:
https://bibliotekanauki.pl/articles/1294693.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
boundary value problems on Riemann surfaces
functional equation
Opis:
The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.
Źródło:
Annales Polonici Mathematici; 1997, 67, 1; 1-14
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 53

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