Stability of difference problems generated by infinite systems of quasilinear parabolic functional differential equations

Abstract

The paper deals with infinite weakly coupled systems of quasilinear parabolic differential functional equations. Initial boundary conditions of the Robin type are considered. We construct an explicit Euler type approximation method based on an infinite system of difference functional equations. Next we apply the truncation method to obtain a finite difference scheme corresponding to the original differential problem. We present a complete convergence analysis for the methods. The results are based on a comparison technique with nonlinear estimates of the Perron type for given functions.