Implicit difference methods for parabolic functional differential equations

Abstract

AbstractWe present a new class of numerical methods for the solution of quasilinear parabolic functional differential equations. The numerical methods are difference schemes which are implicit with respect to time variable. We give a complete convergence analysis for the methods and we show by an example that the new methods are considerable better that the explicit schemes. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. Results obtained in the paper can be applied to differential integral problems and equations with retarded variables.