Solution of a Singular Integral Equation by a Split-Interval Method

Abstract

In this paper we give details of a new numerical method for the solution of a singular integral equation of Volterra type that has an infinite class of solutions. The split-interval method we have adopted utilises a simple robust numerical method over an initial time interval (which includes the singularity) combined with extrapolation. We describe the method and give details of its order of convergence together with examples that show its effectiveness.