Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations. (26th May 2011)

• Record Type: Journal Article
• Authors: Imani, Ahmad; Aminataei, Azim; Imani, Ali
• Other Names: Volodin Andrei Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2011(2011)
• Publication Date: 2011-05-26
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2011/673085
• Languages: English
• ISSNs: 0161-1712

Abstract

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.