Implicit difference schemes for evolution functional differential equations
This paper deals with implicit difference schemes for quasilinear functional differential equations or systems. The paper is divided into two parts. In the first part, a new method of investigation of implicit difference schemes corresponding to initial boundary value problems for quasilinear evolution functional differential equations or systems is proposed. A general implicit difference functional problem with an unknown function of several variables is formulated. Sufficient conditions for the existence and uniqueness of a solution of the initial boundary value problem are given and some error estimates of approximate solutions are established. In the second part, the general results obtained before are applied to quasilinear functional systems with first order partial derivatives and to quasilinear parabolic problems.
scientific article; zbMATH DE number 5862060