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

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. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.