Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domains
Provides a numerical method for solving a specific nonlinear ODE in astrophysics, but the improvement over existing methods is unclear.
The authors propose a Lagrangian method using modified generalized Laguerre functions to solve the Lane-Emden equation on semi-infinite domains, reducing it to algebraic equations. The method yields acceptable solutions compared to known results.
In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian method. The method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with some well-known results and show that the present solution is acceptable.