On the numerical integration of a singular two-point boundary value problem

Abstract

The singular two-point boundary value problem:

y″+2/x y′+f(x,y) = 0, 0<x<1, y′(0) = 0, y(1) = A,

occurs freqently in many applied problems. There has been considerable recent interest by many authors in the development of finite difference and spline approximation methods designed specially for this singular two-point boundary value problem. We report the interesting result that by writing the differential operator suitably, existing finite difference and cubic spline approximation methods for the regular two-point boundary value problem:

u″+φ(x,u) = 0, u(0) = 0, u(1) = A,

can be used for the numerical integration of the singular two-point boundary value problem.

Keywords:

• Singular boundary value problems
• finite difference methods
• Numerov's method
• spline approximations