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

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.