A numerical approach with error estimation to solve general integro-differential-difference equations using Dickson polynomials

Kürkçü Ö. K., ASLAN E., Sezer M.

Applied Mathematics and Computation, vol.276, pp.324-339, 2016 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 276
  • Publication Date: 2016
  • Doi Number: 10.1016/j.amc.2015.12.025
  • Journal Name: Applied Mathematics and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.324-339
  • Keywords: Algorithm, Dickson polynomials, Error estimation, He's variational iteration and homotopy perturbation methods, Integro-differential-difference equations, Matrix methods
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this paper, a matrix method based on the Dickson polynomials and collocation points is introduced for the numerical solution of linear integro-differential-difference equations with variable coefficients under the mixed conditions. In addition, in order to improve the numerical solution, an error analysis technique relating to residual functions is performed. Some linear and nonlinear numerical examples are given to illustrate the accuracy and applicability of the method. Eventually, the obtained results are discussed according to the parameter-α of Dickson polynomials and the residual error estimation.