International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 673085, 11 pages
http://dx.doi.org/10.1155/2011/673085
Research Article

Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations

Ahmad Imani,1 Azim Aminataei,2 and Ali Imani2

1Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran
2Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran 1541849611, Iran

Received 8 December 2010; Accepted 24 March 2011

Academic Editor: Andrei Volodin

Copyright © 2011 Ahmad Imani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We extend a collocation method for solving a nonlinear ordinary differential equation (ODE) via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in chemistry, physics, and so forth, see the works of (Doha and Bhrawy 2006, Guo 2000, and Guo et al. 2002). Choosing the optimal polynomial for solving every ODEs problem depends on many factors, for example, smoothing continuously and other properties of the solutions. In this paper, we show intuitionally that in some problems choosing other members of Jacobi polynomials gives better result compared to Chebyshev or Legendre polynomials.