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Numerical method of bicharacteristics for quasilinear hyperbolic functional differential systems

100%
Kropielnicka K.
Commentationes Mathematicae
|
2005
|
tom 45
|
nr 1
EN
Classical solutions of mixed problems for first order partial functional differential systems in two independent variables are approximated in the paper with solutions of a difference problem of the Euler type. The mesh for the approximate solutions is obtained by a numerical solving of equations of bicharacteristics. The convergence of explicit difference schemes is proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of the Perron type. Differential systems with deviated variables and differential integral systems can be obtained from a general model by specializing given operators.
2
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Generalized solutions of first order partial differential functional inequalities

88%
Czernous W.
Commentationes Mathematicae
|
2006
|
tom 46
|
nr 1
EN
The paper deals with initial boundary value problems for nonlinear first order partial differential functional equations. A theorem on the uniqueness of generalized solutions is proved. It is based on a comparison result for functional differential inequalities in the Carathéodory sense. A theorem on generalized solutions of functional differential inequalities is presented.
3
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Implicit difference methods for infinite systems of hyperbolic functional differential equations

75%
Szafrańska A.
Commentationes Mathematicae
|
2010
|
tom 50
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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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