On the convergence of second-order finite difference method for weakly regular singular boundary value problems

Abstract

The second-order finite difference method developed by Chawla and Katti in 1985 based on a uniform mesh for the singular two-point boundary value problems with , 0≤b 0<1 and boundary conditions y(0)=A, y(1)=B (A, B are finite constants) has been extended for general class of non-negative functions , 0≤b 0<1 and the boundary conditions Second-order convergence of the method has been established for general non-negative function p(x) and under quite general conditions on f(x, y). Our method is based on one evaluation of f and for p(x)=1, it reduces to the classical second-order method for y′′ = f(x, y). In the case of , 0≤b 0<1, this method provides better results than some existing second-order method which is corroborated by one example, and the order of method is also corroborated for general non-negative functions p(x).