A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials

Authors : Tuğçe Mollaoğlu, Mehmet Sezer

Pages : 39-49

Doi:10.18466/cbayarfbe.302638

View : 19 | Download : 7

Publication Date : 2017-03-30

Article Type : Research Paper

Abstract :The main aim of this study is to apply the Gegenbauer polynomials for the solution of high-order linear differential difference equations with functional arguments under initial-boundary conditions.The technique we have used is essentially based on the truncated Gegenbauer series and its matrix representations along with collocation points. Also, by using the Mean-Value Theorem and residual function, an efficient error estimation technique is proposed and some illustrative examples are presented to demonstrate the validity and applicability of the method.
Keywords : Gegenbauer polynomials, Differential difference equations, Collocation method, Matrix method, Error estimation, Residual function