Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations | Zendy

Ahmad Imani | Zendy; A. Aminataei | Zendy; Ali Imani | Zendy

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Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations

Author(s) -

Ahmad Imani,

A. Aminataei,

Ali Imani

Publication year - 2011

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2011/673085

Subject(s) - mathematics , jacobi polynomials , legendre polynomials , orthogonal collocation , chebyshev polynomials , ode , classical orthogonal polynomials , collocation (remote sensing) , collocation method , polynomial , gegenbauer polynomials , ordinary differential equation , chebyshev equation , orthogonal polynomials , chebyshev filter , nonlinear system , differential equation , mathematical analysis , computer science , machine learning , physics , quantum mechanics

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

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