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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Vydáno v:SIAM journal on scientific computing Ročník 28; číslo 5; s. 1716 - 1729
Hlavní autor: Fornberg, Bengt
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2006
Témata:
Applied mathematics
Boundary conditions
Boundary value problems
Eigenvalues
Methods
ISSN:1064-8275, 1095-7197
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1064-8275
1095-7197
DOI:10.1137/040611252