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

Tuğçe Mollaoğlu | Zendy; Mehmet Sezer | Zendy

Open Access

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

Author(s) -

Tuğçe Mollaoğlu,

Mehmet Sezer

Publication year - 2017

Publication title -

celal bayar üniversitesi fen bilimleri dergisi

Language(s) - English

Resource type - Journals

eISSN - 1305-1385

pISSN - 1305-130X

DOI - 10.18466/cbayarfbe.302638

Subject(s) - mathematics , gegenbauer polynomials , residual , mathematical analysis , differential equation , jacobi polynomials , collocation (remote sensing) , classical orthogonal polynomials , boundary value problem , orthogonal polynomials , algorithm , computer science , machine learning

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.

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