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Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions

Published online by Cambridge University Press:  03 June 2015

Yunxia Wei  and
Yanping Chen
Yunxia Wei*
Affiliation:
School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
*
URL: http://202.116.32.252/userinfo.asp?usernamesp=%B3%C2%D1%DE%C6%BC, Email: [email protected]
Corresponding author. Email:[email protected]
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Abstract

The theory of a class of spectral methods is extended to Volterra integro-differential equations which contain a weakly singular kernel (t - s)->* with 0 < μ < 1. In this work, we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth. We provide a rigorous error analysis for the spectral methods, which shows that both the errors of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in L°°-norm and weighted L2-norm. The numerical examples are given to illustrate the theoretical results.

Keywords

45J0565R20Volterra integro-differential equationsweakly singular kernelsspectral methodsconvergence analysis
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 1 , February 2012 , pp. 1 - 20
Copyright
Copyright © Global-Science Press 2012

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