Implicit difference methods for infinite systems of hyperbolic functional differential equations
Commentationes Mathematicae, Tome 50 (2010) no. 1.

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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.
Mots-clés : initial boundary value problems, difference functional equations, difference methods, stability and convergence, interpolating operators, nonlinear estimates of the Perron type 
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Anna Szafrańska. Implicit difference methods for infinite systems of hyperbolic functional differential equations. Commentationes Mathematicae, Tome 50 (2010) no. 1. https://geodesic-test.mathdoc.fr/item/COMA_2010__50_1_292246/