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″+1xy′+f(x,y)=0, 0<x⩽1, y′(0)=0, y(1)=ahas 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.