UNIFORM MESH FINITE DIFFERENCE METHOD FOR A CLASS OF SINGULAR TWO-POINT BOUNDARY VALUE PROBLEMS.

Abstract

A new finite difference method based on uniform mesh is given for the (weakly) singular two-point boundary value problem: (x** alpha **y prime ) prime equals f(x,y), y(0) equals A, y(1) equals B, 0 less than alpha less than 1. Under quite general conditions on f prime and f double prime , it is shown that the present method based on uniform mesh provides O(h**2)-convergent approximations for all alpha belong to (0,1). The method is based on one evaluation of f, and for alpha equals 0 it reduces to the classical second order method for y double prime equals f(x,y).