Approximation of Boundary Value Problem Solutions for Integro-Dierential Equations of the Neutral Type Using a Spline Function Method

Abstract

Boundary value problems for integro-differential equations with a deviating argument are mathematical models of various applied processes in biology, immunology and medicine. Finding solutions to boundary value problems with a time delay in analytical form is possible only in the simplest cases, so the real task is to develop efficient methods for finding their approximate solutions. The goal of this paper is to extend the approximation schemes using cubic splines of defect two for boundary value problems for integro-differential equations with many delays.