On order 5 symplectic explicit Runge-Kutta Nyström methods

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dc.contributor.author Chou, Lin-Yi en
dc.contributor.author Sharp, P. en
dc.date.accessioned 2009-06-12T00:11:23Z en
dc.date.available 2009-06-12T00:11:23Z en
dc.date.issued 2000 en
dc.identifier.citation Journal of Applied Mathematics and Decision Sciences 4 (2), 143-150. 2000 en
dc.identifier.issn 1173-9126 en
dc.identifier.uri http://hdl.handle.net/2292/4324 en
dc.description An open access copy of this article is available and complies with the copyright holder/publisher conditions. en
dc.description.abstract Order five symplectic explicit Runge-Kutta Nyström methods of five stages are known to exist. However, these methods do not have free parameters with which to minimise the principal error coefficients. By adding one derivative evaluation per step, to give either a six-stage non-FSAL family or a seven-stage FSAL family of methods, two free parameters become available for the minimisation. This raises the possibility of improving the efficiency of order five methods despite the extra cost of taking a step. We perform a minimisation of the two families to obtain an optimal method and then compare its numerical performance with published methods of orders four to seven. These comparisons along with those based on the principal error coefficients show the new method is significantly more efficient than the five-stage, order five methods. The numerical comparisons also suggest the new methods can be more efficient than published methods of other orders. en
dc.publisher Hindawi Publishing Corporation en
dc.relation.ispartofseries Journal of Applied Mathematics and Decision Sciences en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/1173-9126/ en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title On order 5 symplectic explicit Runge-Kutta Nyström methods en
dc.type Journal Article en
dc.subject.marsden Fields of Research::230000 Mathematical Sciences::230100 Mathematics en
dc.identifier.doi 10.1155/S1173912600000109 en
pubs.issue 2 en
pubs.begin-page 143 en
pubs.volume 4 en
dc.description.version VoR - Version of Record en
dc.rights.holder Copyright: Hindawi Publishing Corporation en
pubs.end-page 150 en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en


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