Year: 2013
Author: Bernard Bialecki, Ryan I. Fernandes
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 4 : pp. 461–476
Abstract
The alternating direction implicit (ADI) method is a highly efficient technique for solving multi-dimensional time dependent initial-boundary value problems on rectangles. When the ADI technique is coupled with orthogonal spline collocation (OSC) for discretization in space, we not only obtain the global solution efficiently, but the discretization error with respect to space variables can be of an arbitrarily high order. In [2], we used a Crank Nicolson ADI OSC method for solving general nonlinear parabolic problems with Robin's boundary conditions on rectangular polygons and demonstrated numerically the accuracy in various norms. A natural question that arises is: Does this method have an extension to non-rectangular regions? In this paper, we present a simple idea of how the ADI OSC technique can be extended to some such regions. Our approach depends on the transfer of Dirichlet boundary conditions in the solution of a two-point boundary value problem (TPBVP). We illustrate our idea for the solution of the heat equation on the unit disc using piecewise Hermite cubics.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.13-13S05
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 4 : pp. 461–476
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Alternating direction implicit method orthogonal spline collocation two point boundary value problem Crank Nicolson parabolic equation non-rectangular region.
Author Details
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Alternating direction implicit orthogonal spline collocation on some non-rectangular regions with inconsistent partitions
Bialecki, Bernard | Fernandes, Ryan I.Numerical Algorithms, Vol. 74 (2017), Iss. 4 P.1083
https://doi.org/10.1007/s11075-016-0187-7 [Citations: 5] -
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