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Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type

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Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type

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dc.contributor.author Blanes Zamora, Sergio es_ES
dc.contributor.author Casas, Fernando es_ES
dc.contributor.author Mechthild Thalhammer es_ES
dc.date.accessioned 2019-06-01T20:01:01Z
dc.date.available 2019-06-01T20:01:01Z
dc.date.issued 2018 es_ES
dc.identifier.issn 0272-4979 es_ES
dc.identifier.uri http://hdl.handle.net/10251/121413
dc.description.abstract [EN] The main objective of this work is to provide a stability and error analysis of high-order commutator-free quasi-Magnus (CFQM) exponential integrators. These time integration methods for nonautonomous linear evolution equations are formed by products of exponentials involving linear combinations of the defining operator evaluated at certain times. In comparison with other classes of time integration methods, such as Magnus integrators, an inherent advantage of CFQM exponential integrators is that structural properties of the operator are well preserved by the arising linear combinations. Employing the analytical framework of sectorial operators in Banach spaces, evolution equations of parabolic type and dissipative quantum systems are included in the scope of applications. In this context, however, numerical experiments show that CFQM exponential integrators of nonstiff order five or higher proposed in the literature suffer from poor stability properties. The given analysis delivers insight that CFQM exponential integrators are well defined and stable only if the coefficients occurring in the linear combinations satisfy a positivity condition and that an alternative approach for the design of stable high-order schemes relies on the consideration of complex coefficients. Together with suitable local error expansions, this implies that a high-order CFQM exponential integrator retains its nonstiff order of convergence under appropriate regularity and compatibility requirements on the exact solution. Numerical examples confirm the theoretical result and illustrate the favourable behaviour of novel schemes involving complex coefficients in stability and accuracy. es_ES
dc.description.sponsorship Ministerio de Economia y Competitividad (Spain) through projects MTM2013-46553-C3 and MTM2016-77660-P (AEI/FEDER, UE) to S.B. and F.C. es_ES
dc.language Inglés es_ES
dc.publisher Oxford University Press es_ES
dc.relation MINECO/MTM2013-46553-C3-3-P es_ES
dc.relation MINECO/MTM2016-77660-P es_ES
dc.relation.ispartof IMA Journal of Numerical Analysis es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Nonautonomous linear evolution equations es_ES
dc.subject Parabolic initial-boundary value problems es_ES
dc.subject Dissipative quantum systems es_ES
dc.subject Exponential integrators es_ES
dc.subject Magnus integrators es_ES
dc.subject Commutator-free quasi-Magnus exponential integrators es_ES
dc.subject Stability es_ES
dc.subject Local error es_ES
dc.subject Convergence es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1093/imanum/drx012 es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Blanes Zamora, S.; Casas, F.; Mechthild Thalhammer (2018). Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type. IMA Journal of Numerical Analysis. 38(2):743-778. https://doi.org/10.1093/imanum/drx012 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1093/imanum/drx012 es_ES
dc.description.upvformatpinicio 743 es_ES
dc.description.upvformatpfin 778 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 38 es_ES
dc.description.issue 2 es_ES
dc.relation.pasarela 380587 es_ES
dc.contributor.funder Ministerio de Economía y Empresa es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES


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