A numerical approach for solving the high-order linear singular differential-difference equations

Yuezbasi S.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.62, no.5, pp.2289-2303, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 5
  • Publication Date: 2011
  • Doi Number: 10.1016/j.camwa.2011.07.016
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2289-2303
  • Keywords: Singular differential-difference equations, Approximate solutions, Collocation method, Collocation points, The Bessel matrix method, The Bessel polynomials and series, BOUNDARY-VALUE-PROBLEMS, LANE-EMDEN TYPE, HOMOTOPY-PERTURBATION METHOD, VARIATIONAL ITERATION METHOD, ALGORITHM, IVPS
  • Akdeniz University Affiliated: No

Abstract

In this paper, a numerical method which produces an approximate polynomial solution is presented for solving the high-order linear singular differential-difference equations. With the aid of Bessel polynomials and collocation points, this method converts the singular differential-difference equations into the matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. This method gives the analytic solutions when the exact solutions are polynomials. Finally, some experiments and their numerical solutions are given; by comparing the numerical results obtained from the other methods, we show the high accuracy and efficiency of the proposed method. All of the numerical computations have been performed on a PC using some programs written in MATLAB v7.6.0 (R2008a). (C) 2011 Elsevier Ltd. All rights reserved.