A multi-domain spectral collocation method for Volterra integral equations with a weakly singular kernel

In this paper, we introduce a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel. This method is particularly suitable for problems whose solutions contain non-integer exponent factors. We carry out a rigorous error analysis of hp-version in the L-infinity- and weighted L-2-norms. Several numerical examples are presented to demonstrate the efficiency and accuracy of the method. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This paper introduces a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel, particularly suitable for problems with non-integer exponent factors in the solutions. A rigorous error analysis of hp-version in the L-infinity- and weighted L-2-norms is carried out, and several numerical examples are presented to demonstrate the efficiency and accuracy of the method.