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Volume :39 Issue : 2 2012      Add To Cart                                                                    Download

Rational second kind Chebyshev approximation for solving some physical problems on semi-infinite intervals

Auther : M. TAVASSOLI KAJANI , F. GHASEMI TABATABAEI and MOHAMMAD MALEKI

Department of Mathematics, Khorasgan Branch, Islamic Azad University, Isfahan, Iran Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Isfahan, Iran ABSTRACT In this paper, we introduce a new numerical technique to solve some physical problems on a semi-infinite interval. The approach is based on a rational second kind Chebyshev tau method. The operational matrices of derivative and product of rational second kind Chebyshev functions are presented and two nonlinear examples are solved. In the first example, the Volterra's population growth model is formulated as a nonlinear differential equation, and in the second example, the Lane-Emden nonlinear differential equation is considered. Present method is utilized to reduce the solution of these physical problems to the solution of systems of algebraic equations. The method is easy to implement and yields very accurate results. Keywords: Chebyshev polynomials of second kind; rational second kind Chebyshev functions; operational matrix of derivative; the product operational matrix; the Tau method.

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Jun 19, 2012

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