Stability of nonlinear difference functional equations on unbounded domains

Анотація

We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type with an unknown function of several variables. The error is estimated by a solution of an initial problem for nonlinear differential equation.

We apply this general result to the investigation of the stability of difference schemes generated by initial problems for hyperbolic  functional differential equation. We assume nonlinear estimates of the Perron type with respect to functional variable for given operators. Numerical examples are presented.