A Comparative Survey of Numerical Methods for the Linear Generalized Abel Integral Equation

Abstract

AbstractA numerical comparison is made between a number of important representatives of the following classes of methods: (i) collocation, (ii) product integration and (iii) global methods. Special attention is paid to the performance of these methods for problems with a non‐smooth solution. It turned out that, when only relatively low accuracy is required, a good choice would be a second or third order collocation method of Branca. — A new collocation method which accounts for possible non‐smoothness of the solution near the origin, turned out to be advantageous when high accuracy is required, both for problems with a non‐smooth solution, and for problems with a smooth solution.