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The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-differential Equation with a Weakly Singular Kernel

Published online by Cambridge University Press:  28 May 2015

Jie Tang  and
Da Xu
Jie Tang*
Affiliation:
College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, Hunan, P.R. China College of Science, Hunan University of Technology, Zhuzhou 412008, Hunan, P.R. China
Da Xu*
Affiliation:
College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, Hunan, P.R. China
*
Corresponding author.Email address:tj049@163.com
Corresponding author.Email address:daxu@hunnu.edu.cn
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Abstract

The z-transform is introduced to analyze a full discretization method for a partial integro-differential equation (PIDE) with a weakly singular kernel. In this method, spectral collocation is used for the spatial discretization, and, for the time stepping, the finite difference method combined with the convolution quadrature rule is considered. The global stability and convergence properties of complete discretization are derived and numerical experiments are reported.

Keywords

65M1265M1565M7045K05Partial integro-differential equationweakly singular kernelspectral collocation methodsz-transformconvolution quadrature
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 3 , August 2013 , pp. 556 - 570
Copyright
Copyright © Global Science Press Limited 2013

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