Numerical Study of Astrophysics Equations by Meshless Collocation Method Based on Compactly Supported Radial Basis Function

TL;DR

This paper introduces a meshless collocation method using compactly supported radial basis functions to efficiently solve nonlinear singular initial ODEs in astrophysics, demonstrating improved convergence and reliability.

Contribution

The paper presents a novel application of compactly supported radial basis functions with integral operations for solving astrophysics equations on semi-infinite domains.

Findings

Enhanced convergence rate compared to traditional methods

Reduced number of collocation points needed

Results show high accuracy and reliability

Abstract

In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To increase the convergence rate and to decrease the collocation points, we use the compactly supported radial basis function through the integral operations. Afterwards, some special cases of the equation are presented as test examples to show the reliability of the method. Then we compare the results of this work with some results and show that the new method is efficient and applicable