RBF DQ Method for Solving Nonlinear Differential Equations of Lane Emden type

TL;DR

This paper introduces a mesh-less RBF differential quadrature method using Gaussian functions to efficiently and accurately solve nonlinear Lane-Emden type equations on semi-infinite domains, relevant in physics and astrophysics.

Contribution

The paper presents a novel RBF-DQ numerical approach with Gaussian functions for solving Lane-Emden equations, demonstrating improved accuracy and efficiency over existing methods.

Findings

The RBF-DQ method yields highly accurate solutions.

The method outperforms traditional numerical techniques.

It effectively handles semi-infinite domain problems.

Abstract

The Lane-Emden type equations are employed in the modelling of several phenomena in the areas of mathematical physics and astrophysics . In this paper a new numerical method is applied to investigate some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. We will apply a mesh-less method based on radial basis function differential quadrature method. In RBFs-DQ the derivative value of function with respect to a point is directly approximated by a linear combination of all functional values in the global domain . The main aim of this method is the determination of weight coefficients. Here we concentrate on Gaussian(GS) as a radial function for approximating the solution of the mentioned equation. The comparison of the results with the other numerical methods shows the efficiency and accuracy of this method.