Journal
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
Volume 6, Issue 3, Pages 556-570Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/nmtma.2013.1111nm
Keywords
Partial integro-differential equation; weakly singular kernel; spectral collocation methods; z-transform; convolution quadrature
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Funding
- Scientific Research Fund of Hunan Provincial Education Department of China [10C0654]
- NSF of China [10971059, 11101136, 10271046, 10971062]
- NSF of Hunan Province, China [10JJ6003]
- Grant of Science and Technology Commission of Hunan Province, China [2012FJ4116]
- NSF of Hunan University of Technology [2011HZX17]
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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.
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