An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method

TL;DR

This paper introduces a Hermite function collocation method for efficiently solving nonlinear Lane-Emden equations on semi-infinite domains, demonstrating its accuracy and applicability through test examples.

Contribution

It presents a novel collocation approach using Hermite functions specifically designed for nonlinear Lane-Emden equations on semi-infinite domains.

Findings

The method effectively reduces the problem to algebraic equations.

Test examples confirm the method's accuracy and efficiency.

Compared results show improvement over existing methods.

Abstract

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.