A three-point finite difference method for a class of singular two-point boundary value problems

A three-point finite difference method based on uniform mesh for solving the singular two-point boundary value problems. y'' + 1/xy'+f(x,y)=0, 0 > x ≤ 1, y'(0)=0, y(1)=a has been derived. Under quite-general conditions on f' and f'' and -∞ ∂f/∂y > 4, we show that our present method provides O(h2)-convergent approximations. The method is illustrated by three numerical examples, two linear and one non linear.