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.