Approximation of nonlinear differential functional equations

Abstract

We have investigated the approximation of an element with delay in $ {{\mathbb{R}}^n} $ for the case of a continuous input function. We have constructed and substantiated a scheme of the approximation of solutions of an initial-value problem for a nonlinear differential functional equation by the solutions of the Cauchy problem for a system of ordinary differential equations. Calculations for the model example based on the proposed scheme of approximation are in good agreement with well-known results in the literature.