A solution to the Lane-Emden equation inthetheory of stellar structure utilizing the Tau method. (English) Zbl 1275.33021
Summary: We propose a Tau method for solving the singular Lane-Emden equation – a nonlinear ordinary differential equation on a semi-infinite interval. We applied collocation, Galerkin, and Tau methods for solving this problem, and according to the results, the solution of the Tau method is the most accurate. The operational derivative and product matrices of the modified generalized Laguerre functions are presented. These matrices, in conjunction with the Tau method, are then utilized to reduce the solution of the Lane-Emden equation to that of a system of algebraic equations. We also present a comparison of this work with some well-known results and show that the present solution is highly accurate.
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 76M22 | Spectral methods applied to problems in fluid mechanics |
Keywords:
Laguerre functions; nonlinear ODE; Lane-Emden equation; operational derivative; product matricesReferences:
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