Convergence analysis of collocation solutions for delay Volterra integral equations with weakly singular kernels

Abstract

Convergence analysis of the collocation solutions for second-kind Volterra integral equations (VIEs) with weakly singular kernels (WSKs) in continuous piecewise polynomial space (PPS) under certain conditions on the collocation parameters has been established previously. In this paper, we study the analogue convergence analysis for delay Volterra integral equations (DVIEs) with WSKs and vanishing delay. We also investigate the existence, uniqueness and regularity of solution. Finally, we present some illustrative numerical examples to confirm the theoretical results.