On the convergence of finite difference methods for weakly regular singular boundary value problems

The second order finite difference methods M1M1 based on a non-uniform mesh and M2M2 based on an uniform mesh developed by Chawla and Katti [Finite difference methods and their convergence for a class of singular two point boundary value problems, Numer. Math. 39 (1982) 341–350] for weakly regular singular boundary value problems (p(x)y′)′=f(x,y)(p(x)y′)′=f(x,y), 0