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

Year 2017, , 39 - 49, 29.03.2017

Tuğçe Mollaoğlu Mehmet Sezer

https://doi.org/10.18466/cbayarfbe.302638

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

References

• M. T. Rashed, Numerical solution of functional differential,integral and integro- differential equations, Appl.Math.Comput.156 (2004) 485-492.