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Difference functional inequalities and applications

Szafrańska A.

Opuscula Mathematica

2014

Vol. 34, no. 2

405--423

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.

Difference methods for infinite systems of hyperbolic functional differential equations on the Haar pyramid

Jaruszewska-Walczak D.

Opuscula Mathematica

2004

Vol. 24, no. 1

85-96

We consider the Cauchy problem for infinite system of differential functional equations ∂tzk(t, x) = fk(t, x, z, ∂xzk(t, x)), k mem N. In the paper we consider a general class of difference methods for this problem. We prove the convergence of methods under the assumptions that given functions satisfy the nonlinear estimates of the Perron type with respect to functional variables. The proof is based on functional difference inequalities. We constructed the Euler method as an example of difference method.