An approximation algorithm for the solution of the Lane-Emden type equations arising in astrophysics and engineering using Hermite polynomials

Abstract

The purpose of this paper is to propose an efficient numerical method for solving Lane-Emden type equations arising in astrophysics using Hermit polynomials. Our method depends on collocation method. This method based on first taking the truncated Hermite series of the solution function in the Lane-Emden equation and then, transforms Lane-Emden type equation and given conditions into a matrix equation and then, we have the system of linear or nonlinear algebraic equation using collocation points. Then, solving the system of algebraic equations and we have the coefficients of the truncated Hermite series. Some illustrative examples are given to demonstrate the efficiency and validity of the proposed algorithm.