A Note on Fourth Order Method for Doubly Singular Boundary Value Problems

Abstract

We present a fourth order finite difference method for doubly singular boundary value problem (p(x)y′(x))′=q(x)f(x,y),  0<x  ≤1 with boundary conditions y(0)=A (or  y'(0)=0  or  limx→0p(x)y'(x)=0) and αy(1)+ βy'(1)=γ, where α(>0),  β(≥0),  γ and A are finite constants. Here p(0)=0 and q(x) is allowed to be discontinuous at the singular point x=0. The method is based on uniform mesh. The accuracy of the method is established under quite general conditions and also corroborated through one numerical example.