A Pseudospectral Fictitious Point Method for High Order Initial‐Boundary Value Problems

When pseudospectral approximations are used for space derivatives, one often encounters spurious eigenvalues. These can lead to severe time stepping difficulties for PDEs. This is especially the case for equations with high order derivatives in space, requiring multiple conditions at one or both bou...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 28; no. 5; pp. 1716 - 1729
Main Author: Fornberg, Bengt
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2006
Subjects:
Applied mathematics
Boundary conditions
Boundary value problems
Eigenvalues
Methods
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:When pseudospectral approximations are used for space derivatives, one often encounters spurious eigenvalues. These can lead to severe time stepping difficulties for PDEs. This is especially the case for equations with high order derivatives in space, requiring multiple conditions at one or both boundaries. We note here that a very simple-to-implement fictitious point approach circumvents most of these difficulties. The new approach is tested on the Kuramoto-Sivashinsky equation and on a dispersive linear PDE featuring a time-space corner singularity.
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ISSN:1064-8275
1095-7197
DOI:10.1137/040611252