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

TL;DR

This paper introduces a Lagrangian method using Modified generalized Laguerre functions to efficiently solve the nonlinear Lane-Emden equation on semi-infinite domains, reducing it to algebraic equations.

Contribution

The paper presents a novel Lagrangian approach based on Modified generalized Laguerre functions for solving Lane-Emden equations on semi-infinite intervals.

Findings

The method effectively solves the Lane-Emden equation.

Results are consistent with known solutions.

The approach simplifies the problem to algebraic equations.

Abstract

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.