A numerical approach with residual error estimation for solution of high-order linear differential-difference equations by using Gegenbauer polynomials

Abstract

The main aim of this study is to apply the Gegenbauer polynomials for the solution of high-order lineardifferential difference equations with functional arguments under initial-boundary conditions.The technique wehave used is essentially based on the truncated Gegenbauer series and its matrix representations along withcollocation points. Also, by using the Mean-Value Theorem and residual function, an efficient error estimationtechnique is proposed and some illustrative examples are presented to demonstrate the validity and applicabilityof the method.