Algorithms for the effective choice of k in the rational basis for solving second-kind abel intergral equations

Abstract

The $R_{1,1}$ rational functions have been used as bases in a product integration method for solving second-kind Abel integral equations with nonsmooth solutions. Three approximation methods are introduced to determine the bias of k in the rational basis function and the free parameter k is chosen according to the three creteria. The main purpose of this thesis is to develop fast algorithms to determine the free parameter k and investigate the effect of k on the accuracy of the approximation through several problems.