Two Meshfree Numerical Approaches for Solving High-Order Singular Emden–Fowler Type Equations

Abstract

In this paper we suggest indirect radial basis function collocation and radial basis function differential quadrature methods for solving high-order singular Emden–Fowler equations. Here, we concentrate on Gaussian (GA, $$\exp (-c^2 r^2)$$ ) as a radial function for approximating the solution of the mentioned equations. In order to overcome the difficulty of the singular point ( $$x=0$$ ), the Head dense points with dense parameter $$\vartheta $$ and shifted Chebyshev points have been handled. The comparison between the numerical and exact results shows the efficiency and accuracy of these methods and also demonstrate these methods have good convergence rate.