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Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations

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  • Ahmad Imani
  • Azim Aminataei
  • Ali Imani

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.

Suggested Citation

  • Ahmad Imani & Azim Aminataei & Ali Imani, 2011. "Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-11, May.
    • Handle: RePEc:hin:jijmms:673085
    DOI: 10.1155/2011/673085
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    Cited by:

    1. Tafakkori–Bafghi, M. & Loghmani, G.B. & Heydari, M., 2022. "Numerical solution of two-point nonlinear boundary value problems via Legendre–Picard iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 133-159.

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