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Volume 6, Issue 3
The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel

Jie Tang & Da Xu

DOI: 10.4208/nmtma.2013.1111nm

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 556-570.

Published online: 2013-06

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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

Partial integro-differential equation, weakly singular kernel, spectral collocation methods, $z$-transform, convolution quadrature.

  • AMS Subject Headings

65M12, 65M15, 65M70, 45K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-556, author = {Jie Tang and Da Xu}, title = {The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {3}, pages = {556--570}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.1111nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5918.html} }
TY - JOUR T1 - The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel AU - Jie Tang & Da Xu JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 556 EP - 570 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.1111nm UR - https://global-sci.org/intro/article_detail/nmtma/5918.html KW - Partial integro-differential equation, weakly singular kernel, spectral collocation methods, $z$-transform, convolution quadrature. AB -

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.

Jie Tang and Da Xu. (2013). The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel. Numerical Mathematics: Theory, Methods and Applications. 6 (3). 556-570. doi:10.4208/nmtma.2013.1111nm
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