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dc.contributor.authorBlanes, Sergio
dc.contributor.authorCasas, Fernando
dc.contributor.authorChartier, Philippe
dc.contributor.authorMurua, Ander
dc.date.accessioned2014-06-20T10:55:23Z
dc.date.available2014-06-20T10:55:23Z
dc.date.issued2013
dc.identifier.citationBLANES, Sergio, et al. Optimized high-order splitting methods for some classes of parabolic equations. Mathematics of Computation, 2013, vol. 82, no 283, p. 1559-1576.ca_CA
dc.identifier.issn0025-5718
dc.identifier.issn1088-6842
dc.identifier.urihttp://hdl.handle.net/10234/95572
dc.description.abstractWeareconcernedwiththenumericalsolutionobtainedbysplitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. It has been demonstrated that this second-order barrier can be overcome by using splitting methods with complex-valued coefficients (with positive real parts). In this way, methods of orders 3 to 14 by using the Suzuki–Yoshida triple (and quadruple) jump composition procedure have been explicitly built. Here we reconsider this technique and show that it is inherently bounded to order 14 and clearly sub-optimal with respect to error constants. As an alternative, we solve directly the algebraic equations arising from the order conditions and construct methods of orders 6 and 8 that are the most accurate ones available at present time, even when low accuracies are desired. We also show that, in the general case, 14 is not an order barrier for splitting methods with complex coefficients with positive real part by building explicitly a method of order 16 as a composition of methods of order 8.ca_CA
dc.description.sponsorShipThe work of the first, second and fourth authors was partially supported by Ministerio de Ciencia e Innovación (Spain) under the coordinated project MTM2010-18246-C03 (co-financed by FEDER Funds of the European Union). Financial support from the “Acción Integrada entre España y Francia” HF2008-0105 was also acknowledged The fourth author was additionally funded by project EHU08/43 (Universidad del País Vasco/Euskal Herriko Unibertsitatea).ca_CA
dc.format.extent15 p.ca_CA
dc.format.mimetypeapplication/pdfca_CA
dc.language.isoengca_CA
dc.publisherAmerican Mathematical Societyca_CA
dc.relation.isPartOfMathematics of Computation, 2013, vol. 82, no 283ca_CA
dc.rights© Copyright American Mathematical Societyca_CA
dc.subjectComposition methodsca_CA
dc.subjectSplitting methodsca_CA
dc.subjectComplex coefficientsca_CA
dc.subjectParabolic evolution equationsca_CA
dc.titleOptimized high-order splitting methods for some classes of parabolic equationca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttp://dx.doi.org/10.1090/S0025-5718-2012-02657-3
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_CA
dc.relation.publisherVersionhttp://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2012-02657-3/home.htmlca_CA


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