A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems

We present a three-point finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problem (x(alpha)y ')' = f(x,y) y(0) = A, y(1) = B, 0 less than or equal to alpha <1. We show that the method, based on non-uniform mesh, provides O(h(4))-convergent approximations. This method is illustrated by two numerical examples, one is linear and the other is non-linear. (C) 2001 Elsevier Science B.V. All rights reserved.