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Zbl 1063.65146
Parand, K.; Razzaghi, M.
Rational Legendre approximation for solving some physical problems on semi-infinite intervals. (English)
[J] Phys. Scr. 69, No. 5, 353-357 (2004). ISSN 0031-8949; ISSN 1402-4896/e

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 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations
92D25 Population dynamics
65L10 Boundary value problems for ODE (numerical methods)
34B05 Linear boundary value problems of ODE
65L60 Finite numerical methods for ODE

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

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Zentralblatt MATH Berlin [Germany]