Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels

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.

Author Details

Xiulian Shi

Yanping Chen