Rational legendre approximation for solving some physical problems on semi-infinite intervals

A numerical technique for solving some physical problems on a semi-infinite interval is presented. Two nonlinear examples are proposed. In the first example the Volterra's population model growth is formulated as a nonlinear differential equation, and in the second example the Lane-Emden nonlinear differential equation is considered. The approach is based on a rational Legendre tau method. The operational matrices of derivative and product of rational Legendre functions are presented. These matrices together with the tau method are 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.