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

摘要

We present a new three-point finite difference method based on 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 uniform mesh, provides O(h4)-convergent approximations. This method is illustrated by two numerical examples, one is linear and another is non-linear.