A numerical method for singular two point boundary value problems via Chebyshev economizition

Abstract

In this paper we present a numerical method for solving a two point boundary value problem in the interval [0,1] with regular singularity at x=0. By employing the Chebyshev economizition on [0,δ], where δ is near the singularity, we first replace it by a regular problem on some interval [δ,1]. The stable central difference method is then employed to solve the problem over the reduced interval. Some numerical results are presented to demonstrate the applicability of the method.