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Piecewise Legendre spectral-collocation method for Volterra integro-differential equations

Part of: Integro-ordinary differential equations Miscellaneous special kernels Partial differential equations, initial value and time-dependent initial-boundary value problems Volterra integral equations

Published online by Cambridge University Press:  01 April 2015

Zhendong Gu  and
Yanping Chen
Zhendong Gu
Affiliation:
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China email guzhd@qq.com
Yanping Chen
Affiliation:
School of Mathematics Science, South China Normal University, Guangzhou 510631, China email yanpingchen@scnu.edu.cn

Abstract

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Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in $h^{m}N^{-m}$-version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.

MSC classification

Primary: 65M70: Spectral, collocation and related methods
Secondary: 45D05: Volterra integral equations 45J05: Integro-ordinary differential equations
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 231 - 249
Copyright
© The Author(s) 2015 

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