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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/11955

Title: Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term
Authors: PANI, AK
FAIRWEATHER, G
FERNANDES, RI
Keywords: integro-differential equation
time discretization
integrodifferential equation
laplace transformation
parabolic type
scheme
Issue Date: 2008
Publisher: SIAM PUBLICATIONS
Citation: SIAM JOURNAL ON NUMERICAL ANALYSIS, 46(1), 344-364
Abstract: New numerical techniques are presented for the solution of a class of linear partial integro-differential equations (PIDEs) with a positive-type memory term in the unit square. In these methods, orthogonal spline collocation (OSC) is used for the spatial discretization, and, for the time stepping, new alternating direction implicit (ADI) methods based on the backward Euler, the Crank-Nicolson, and the second order BDF methods combined with judiciously chosen quadrature rules are considered. The ADI OSC methods are proved to be of optimal accuracy in time and in the L(2) norm in space. Numerical results confirm the predicted convergence rates and also exhibit optimal accuracy in the L(infinity) and H(1) norms and superconvergence phenomena.
URI: http://dx.doi.org/10.1137/050634967
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11955
http://hdl.handle.net/10054/11955
ISSN: 0036-1429
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