A numerical scheme for solutions of the Chen system


YÜZBAŞI Ş.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.35, no.8, pp.885-893, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 8
  • Publication Date: 2012
  • Doi Number: 10.1002/mma.1581
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.885-893
  • Keywords: Chen system, Bessel collocation method, approximate solution, nonlinear differential equation systems, Bessel polynomials and series, collocation points, CHAOTIC DYNAMICAL-SYSTEM, FREDHOLM INTEGRODIFFERENTIAL EQUATIONS, INTEGRAL-EQUATIONS
  • Akdeniz University Affiliated: No

Abstract

In this paper, we will develop the Bessel collocation method to find approximate solutions of the Chen system, which is a three-dimensional system of ODEs with quadratic nonlinearities. This scheme consists of reducing the problem to a nonlinear algebraic equation system by expanding the approximate solutions by means of the Bessel polynomials with unknown coefficients. By help of the collocation points and the matrix operations of derivatives, the unknown coefficients of the Bessel polynomials are calculated. The accuracy and efficiency of the proposed approach are demonstrated by two numerical examples and performed with the aid of a computer code written in MAPLE. In addition, comparisons between our method and the homotopy perturbation method numerical solutions are made with the accuracy of solutions. Copyright (C) 2012 John Wiley & Sons, Ltd.