Computation of Optimal Monotonicity Preserving General Linear Methods

Handle URI:
http://hdl.handle.net/10754/138431
Title:
Computation of Optimal Monotonicity Preserving General Linear Methods
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X )
Abstract:
Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Mathematics Group
Publisher:
Mathematics of Computation
Journal:
Mathematics of Computation
Issue Date:
Jul-2009
DOI:
10.1090/S0025-5718-09-02209-1
Type:
Article
ISSN:
0025-5718
Appears in Collections:
Articles; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKetcheson, David I.en
dc.date.accessioned2011-07-30T11:41:10Z-
dc.date.available2011-07-30T11:41:10Z-
dc.date.issued2009-07en
dc.identifier.issn0025-5718en
dc.identifier.doi10.1090/S0025-5718-09-02209-1en
dc.identifier.urihttp://hdl.handle.net/10754/138431en
dc.description.abstractMonotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.en
dc.language.isoenen
dc.publisherMathematics of Computationen
dc.titleComputation of Optimal Monotonicity Preserving General Linear Methodsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Mathematics Groupen
dc.identifier.journalMathematics of Computationen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorKetcheson, David I.en
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