Int. J. Appl. Comput. Math DOI 10.1007/s40819-017-0368-7 ORIGINAL PAPER Two Meshfree Numerical Approaches for Solving High-Order Singular Emden–Fowler Type Equations Kourosh Parand 1 · Mohammad Hemami 1 · Soleiman Hashemi-Shahraki 1 © Springer India Pvt. Ltd. 2017 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 ϑ and shifted Cheby- shev 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. Keywords Radial basis function · Collocation · Differential quadrature · Emden–Fowler equations · High-order · Singularity Mathematics Subject Classification 34A12 · 34A34 · 65L05 Introduction In expression of various phenomena of sciences, Emden–Fowler equation is a classic famous equation as follows: d 2 f dx 2 + α x df dx + h(x )g( f ) = 0, f (0) = γ, df dx | x =0 = 0, (1) B Mohammad Hemami mohammadhemami@yahoo.com Kourosh Parand k_parand@sbu.ac.ir Soleiman Hashemi-Shahraki soleiman.hashemi.sh@gmail.com 1 Department of Computer Sciences, Shahid Beheshti University, G.C., Tehran 19697-64166, Iran 123