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Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term

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Title Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term
 
Creator PANI, AK
FAIRWEATHER, G
FERNANDES, RI
 
Subject integro-differential equation
time discretization
integrodifferential equation
laplace transformation
parabolic type
scheme
evolution equation with positive-type memory term
alternating direction implicit method
orthogonal spline collocation
backward euler method
crank-nicolson method
second order backward differentiation formula method
quadrature rules
optimal order convergence.
 
Description 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.
 
Publisher SIAM PUBLICATIONS
 
Date 2011-08-29T04:20:19Z
2011-12-26T12:58:24Z
2011-12-27T05:48:15Z
2011-08-29T04:20:19Z
2011-12-26T12:58:24Z
2011-12-27T05:48:15Z
2008
 
Type Article
 
Identifier SIAM JOURNAL ON NUMERICAL ANALYSIS, 46(1), 344-364
0036-1429
http://dx.doi.org/10.1137/050634967
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11955
http://hdl.handle.net/10054/11955
 
Language en