Approximate solution of singular integral equations

An approximate method is developed for solving singular integral equations of the first kind, over a finite interval. The singularity is assumed to be of the Cauchy type, and the four basically different cases of singular integral equations of practical occurrence are dealt with simultaneously. The presently obtained results are found to be in complete agreement with the known analytical solutions of simple equations. The methodology of the present work is expected to be useful for solving singular integral equations of the first kind, involving partly singular and partly regular kernels, as well as equations of the second kind involving similar kernels, with appropriate adjustments regarding the endpoint behaviours of the unknown function. (C) 2004 Elsevier Ltd. All rights reserved.