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Numerical approximations of parabolic functional differential equations on unbounded domains

100%
Baranowska A.
Commentationes Mathematicae
|
2007
|
tom 47
|
nr 2
EN
The paper is concerned with initial problems for nonlinear parabolic functional differential equations. A general class of difference methods is constructed. A theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type with an unknown function of several variables is presented. The convergence of explicit difference schemes is proved by means of consistency and stability arguments. It is assumed that given function satisfy nonlinear estimates of the Perron type with respect to a functional variable. Results obtained in the paper can be applied to differential integral problems and equations with retarded variables. Numerical examples are presented.
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Implicit difference methods for infinite systems of hyperbolic functional differential equations

75%
Szafrańska A.
Commentationes Mathematicae
|
2010
|
tom 50
|
nr 1
EN
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.
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