Solution of a singular integral equation by a split-interval method
Teresa Diogo 1, Neville J. Ford 2, Pedro M. Lima 1, Sophy M. Thomas 21 Department of Mathematics, Instituto Superior Técnico, Lisbon, Portugal
2 Department of Mathematics, University of Chester, Chester, CH1 4BJ, UK
Received by the editors January 25, 2005 and revised January 10, 2006
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 simpler 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.
AMS subject classifications: 65R20
Key words: numerical methods; extrapolation; singular integral equation; Volterra equation