Displaying similar documents to “Implicit difference schemes for mixed problems related to parabolic functional differential equations”

Comparison of explicit and implicit difference schemes for parabolic functional differential equations

Zdzisław Kamont, Karolina Kropielnicka (2012)

Annales Polonici Mathematici

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Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both...

Difference methods for parabolic functional differential problems of the Neumann type

K. Kropielnicka (2007)

Annales Polonici Mathematici

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Nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type are considered. A general class of difference methods for the problem is constructed. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given...

Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis

A. Poliński (2006)

Annales Polonici Mathematici

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We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.

Implicit difference methods for quasilinear parabolic functional differential problems of the Dirichlet type

K. Kropielnicka (2008)

Applicationes Mathematicae

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Classical solutions of quasilinear functional differential equations are approximated with solutions of implicit difference schemes. Proofs of convergence of the difference methods are based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions are used. Numerical examples are given.

A new compact finite difference quasilinearization method for nonlinear evolution partial differential equations

P.G. Dlamini, M. Khumalo (2017)

Open Mathematics

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This article presents a new method of solving partial differential equations. The method is an improvement of the previously reported compact finite difference quasilinearization method (CFDQLM) which is a combination of compact finite difference schemes and quasilinearization techniques. Previous applications of compact finite difference (FD) schemes when solving parabolic partial differential equations has been solely on discretizing the spatial variables and another numerical technique...

Generalized method of lines for first order partial functional differential equations

W. Czernous (2006)

Annales Polonici Mathematici

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Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. ...

Numerical approximations of parabolic differential functional equations with the initial boundary conditions of the Neumann type

Roman Ciarski (2004)

Annales Polonici Mathematici

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The aim of this paper is to present a numerical approximation for quasilinear parabolic differential functional equations with initial boundary conditions of the Neumann type. The convergence result is proved for a difference scheme with the property that the difference operators approximating mixed derivatives depend on the local properties of the coefficients of the differential equation. A numerical example is given.

Comparison of explicit and implicit difference methods for quasilinear functional differential equations

W. Czernous, Z. Kamont (2011)

Applicationes Mathematicae

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We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties...

Implicit difference methods for nonlinear first order partial functional differential systems

Elżbieta Puźniakowska-Gałuch (2010)

Applicationes Mathematicae

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Initial problems for nonlinear hyperbolic functional differential systems are considered. Classical solutions are approximated by solutions of suitable quasilinear systems of difference functional equations. The numerical methods used are difference schemes which are implicit with respect to the time variable. Theorems on convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability is based on a comparison technique with nonlinear...