A fast-converging recursive approach for Lane–Emden type initial value problems arising in astrophysics

Abstract

In this paper, we describe a new technique, called the least square recursive approach (LSRA), to approximate the solution of Lane–Emden type initial value problems, which describe many phenomena in mathematical physics and astrophysics. The proposed method reduces the solution of the original initial value problem to the solution of an integral equation and provides us with a simple way to improve the convergence of the solution. Convergence analysis of the method is carried out. The obtained results are compared with exiting methods (Chowdhary and Hashim, 2007; Wazwaz, 2001; Singh et al., 2009) to show the advantage of the proposed method. The method is shown to be very reliable, accurate and computationally efficient.