RBF-DQ method for solving non-linear differential equations of Lane-Emden type

Abstract

The Lane-Emden type equations are employed in the modeling 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 non-linear ordinary differential equations on the semi-infinite domain [0,∞). We will apply a meshless method based on radial basis function differential quadrature (RBF-DQ) 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. Keywords: Radial basis functions, RBFs-DQ, Lane-Emden type equations, Gaussian, Semi-infinite