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

AbstractThe second order finite difference methods M1 based on a non-uniform mesh and M2 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), 0<x⩽1, with p(x)=xb0, 0⩽b0<1, and boundary conditions y(0)=A, y(1)=B (A, B are finite constants) have been extended for general class of nonnegative functions p(x)=xb0g(x), 0⩽b0