Solving Stiff Differential Equations with the Method of Patches

We introduce a new method for solving very stiff sets of ordinary differential equations. The basic idea is to replace the original nonlinear equations with a set of equally stiff equations that are piecewise linear, and therefore can be solved exactly. We demonstrate the value of the method on smal...

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Bibliographic Details
Published inJournal of computational physics Vol. 144; no. 2; pp. 280 - 298
Main Authors Brydon, David, Pearson, John, Marder, Michael
Format Journal Article
LanguageEnglish
Published Elsevier Inc 10.08.1998
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Summary:We introduce a new method for solving very stiff sets of ordinary differential equations. The basic idea is to replace the original nonlinear equations with a set of equally stiff equations that are piecewise linear, and therefore can be solved exactly. We demonstrate the value of the method on small systems of equations for which some other methods are inefficient or produce spurious solutions, estimate error bounds, and discuss extensions of the method to larger systems of equations and to partial differential equations.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0021-9991
1090-2716
DOI:10.1006/jcph.1998.6008