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(xαy′)′=f(x,y)y(0)=A, y(1)=B, 0⩽α<1.We show that the method, based on non-uniform mesh, provides O(h4)-convergent approximations. This method is illustrated by two numerical examples, one is linear and the other is non-linear.