Numerical solution of a singular boundary value problem for a generalized Emden–Fowler equation

Abstract

In this paper we shall deal with an equation of the form y″(x)=−g(x)x p y(x) q, where p and q are real parameters satisfying p>−2, q<−1 and g is a positive and continuous function on [0,1]. We shall search for positive solutions which satisfy the boundary conditions: y(0)=y(1)=0. The initial nonlinear problem is transformed into a sequence of linear ones, each one of them is approximated by a finite difference scheme. Asymptotic expansions of the error are obtained and numerical examples are then analysed.