Rational Chebyshev of Second Kind Collocation Method for Solving a Class of Astrophysics Problems

TL;DR

This paper introduces a collocation method using Rational Chebyshev of Second Kind functions to efficiently solve the Lane-Emden equation over semi-infinite intervals, relevant in astrophysics and mathematical physics.

Contribution

The study develops and demonstrates a novel collocation approach with RSC functions for solving the Lane-Emden equation on semi-infinite domains, showing improved efficiency.

Findings

Method is efficient and applicable for Lane-Emden equations.

Provides accurate solutions over semi-infinite intervals.

Compared favorably with previous methods.

Abstract

The Lane-Emden equation has been used to model several phenomenas in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the Rational Chebyshev of Second Kind function (RSC) to solve the Lane-Emden equation over the semi-infinit interval [0; +infinity). According to well-known results and comparing with previous methods, it can be said that this method is efficient and applicable.