Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels
Year: 2016
Author: Xiulian Shi, Yanping Chen
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 4 : pp. 648–669
Abstract
A spectral Jacobi-collocation approximation is proposed for Volterra delay integro-differential equations with weakly singular kernels. In this paper, we consider the special case that the underlying solutions of equations are sufficiently smooth. We provide a rigorous error analysis for the proposed method, which shows that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in $L^∞$ norm and weighted $L^2$ norm. Finally, two numerical examples are presented to demonstrate our error analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1088
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 4 : pp. 648–669
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Volterra integro-differential equations spectral Jacobi-collocation method pantograph delay weakly singular kernel.