Legendre spectral Galerkin method for second-kind Volterra integral equations

The Legendre spectral Galerkin method for the Volterra integral equations of the second kind is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the L 2 norm) will decay exponentially provided that the kernel function...

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Bibliographic Details
Published in:Frontiers of mathematics in China 2009-03, Vol.4 (1), p.181-193
Main Authors: Wan, Zhengsu, Chen, Yanping, Huang, Yunqing
Format: Article
Language:English
Subjects:
Approximation
Calculus
Integral equations
Mathematics
Mathematics and Statistics
Methods
Research Article
Studies
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Summary:The Legendre spectral Galerkin method for the Volterra integral equations of the second kind is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the L 2 norm) will decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical examples are given to illustrate the theoretical results.
ISSN:1673-3452
1673-3576
DOI:10.1007/s11464-009-0002-z