Optimal stability polynomials for numerical integration of initial value problems

Handle URI:
http://hdl.handle.net/10754/333599
Title:
Optimal stability polynomials for numerical integration of initial value problems
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X ) ; Ahmadia, Aron ( 0000-0002-2573-2481 )
Abstract:
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Mathematics Group
Citation:
Optimal stability polynomials for numerical integration of initial value problems 2012, 7 (2):247 Communications in Applied Mathematics and Computational Science
Publisher:
Mathematical Sciences Publishers
Journal:
Communications in Applied Mathematics and Computational Science
Issue Date:
8-Jan-2013
DOI:
10.2140/camcos.2012.7.247
ARXIV:
arXiv:1201.3035
Type:
Article
ISSN:
2157-5452; 1559-3940
Additional Links:
http://msp.org/camcos/2012/7-2/p04.xhtml; http://github.com/ketch/RK-opt; http://arxiv.org/abs/1201.3035
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.contributor.authorAhmadia, Aronen
dc.date.accessioned2014-11-03T16:17:27Z-
dc.date.available2014-11-03T16:17:27Z-
dc.date.issued2013-01-08en
dc.identifier.citationOptimal stability polynomials for numerical integration of initial value problems 2012, 7 (2):247 Communications in Applied Mathematics and Computational Scienceen
dc.identifier.issn2157-5452en
dc.identifier.issn1559-3940en
dc.identifier.doi10.2140/camcos.2012.7.247en
dc.identifier.urihttp://hdl.handle.net/10754/333599en
dc.description.abstractWe consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.en
dc.language.isoenen
dc.publisherMathematical Sciences Publishersen
dc.relation.urlhttp://msp.org/camcos/2012/7-2/p04.xhtmlen
dc.relation.urlhttp://github.com/ketch/RK-opten
dc.relation.urlhttp://arxiv.org/abs/1201.3035en
dc.rightsArchived with thanks to Communications in Applied Mathematics and Computational Scienceen
dc.subjectabsolute stabilityen
dc.subjectinitial value problemsen
dc.subjectRunge–Kutta methodsen
dc.titleOptimal stability polynomials for numerical integration of initial value problemsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Mathematics Groupen
dc.identifier.journalCommunications in Applied Mathematics and Computational Scienceen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxividarXiv:1201.3035en
kaust.authorKetcheson, David I.en
kaust.authorAhmadia, Aronen
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