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A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel

Published online by Cambridge University Press:  28 May 2015

Yunxia Wei  and
Yanping Chen
Yunxia Wei*
Affiliation:
College ofMathematic and Information Science, Shandong Institute of Business and Technology, Yantai 264005, Shandong, China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China
*
Corresponding author.Email address:yunxiawei@126.com
Corresponding author.Email address:yanpingchen@scnu.edu.cn
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Abstract

This paper is concerned with obtaining an approximate solution and an approximate derivative of the solution for neutral Volterra integro-differential equation with a weakly singular kernel. The solution of this equation, even for analytic data, is not smooth on the entire interval of integration. The Jacobi collocation discretization is proposed for the given equation. A rigorous analysis of error bound is also provided which theoretically justifies that both the error of approximate solution and the error of approximate derivative of the solution decay exponentially in L∞ norm and weighted L2 norm. Numerical results are presented to demonstrate the effectiveness of the spectral method.

Keywords

65R2045J0565N12Neutral Volterra integro-differential equationweakly singular kernelJacobi collocation discretizationconvergence analysis
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 2 , May 2013 , pp. 424 - 446
Copyright
Copyright © Global Science Press Limited 2013

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