Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domains

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.

💡 Research Summary

The paper addresses the numerical solution of the Lane‑Emden equation, a nonlinear second‑order ordinary differential equation that models the structure of self‑gravitating polytropic spheres in astrophysics. The equation is defined on the semi‑infinite interval (