General Linear Methods for the Numerical Solution of Functional-Differential Equations

Abstract

We construct a general linear scheme for the numerical solution of delay differential equations of the general form, also known as functional-differential equations. This scheme differs from the counterpart of itself for ordinary differential equations in that it involves an intermediate space between the discrete numerical model and the original functional system. We obtain sufficient conditions as well as necessary and sufficient conditions for the convergence rate of our methods. We also present examples showing how analogs of some of the most frequently used numerical methods are covered by the general scheme.