Solution of the generalized Emden–Fowler equations by the hybrid functions method

Abstract

In this paper, we present a numerical algorithm for solving the generalized Emden–Fowler equations, which have many applications in mathematical physics and astrophysics. The method is based on hybrid functions approximations. The properties of hybrid functions, which consist of block-pulse functions and Lagrange interpolating polynomials, are presented. These properties are then utilized to reduce the computation of the generalized Emden–Fowler equations to a system of nonlinear equations. The method is easy to implement and yields very accurate results.