Rational Legendre approximation for solving some physical problems on semi-infinite intervals. (English) Zbl 1063.65146

Parand, K.; Razzaghi, M.

Phys. Scr. 69, No. 5, 353-357 (2004).

Summary: 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.

MSC:

65R20	Numerical methods for integral equations
45J05	Integro-ordinary differential equations
45G10	Other nonlinear integral equations
92D25	Population dynamics (general)
65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B05	Linear boundary value problems for ordinary differential equations
65L60	Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations

Keywords:

numerical examples; Volterra’s population model; nonlinear differential equation; Lane-Emden nonlinear differential equation; rational Legendre tau method