- -

Error analysis of splitting methods for the time dependent Schrodinger equation

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Error analysis of splitting methods for the time dependent Schrodinger equation

Mostrar el registro sencillo del ítem

Ficheros en el ítem

dc.contributor.author Blanes Zamora, Sergio es_ES
dc.contributor.author Casas, Fernando es_ES
dc.contributor.author Murua, Ander es_ES
dc.date.accessioned 2013-05-14T10:44:57Z
dc.date.available 2013-05-14T10:44:57Z
dc.date.issued 2011
dc.identifier.issn 1064-8275
dc.identifier.uri http://hdl.handle.net/10251/28825
dc.description.abstract A typical procedure to integrate numerically the time dependent Schrodinger equation involves two stages. In the first stage one carries out a space discretization of the continuous problem. This results in the linear system of differential equations idu/dt = Hu, where H is a real symmetric matrix, whose solution with initial value u(0) = u(0) is an element of C-N is given by u(t) = e(-itH)u(0). Usually, this exponential matrix is expensive to evaluate, so that time stepping methods to construct approximations to u from time t(n) to t(n+1) are considered in the second phase of the procedure. Among them, schemes involving multiplications of the matrix H with vectors, such as Lanczos and Chebyshev methods, are particularly efficient. In this work we consider a particular class of splitting methods which also involves only products Hu. We carry out an error analysis of these integrators and propose a strategy which allows us to construct different splitting symplectic methods of different order (even of order zero) possessing a large stability interval that can be adapted to different space regularity conditions and different accuracy ranges of the spatial discretization. The validity of the procedure and the performance of the resulting schemes are illustrated in several numerical examples. es_ES
dc.description.sponsorship Submitted to the journal's Methods and Algorithms for Scientific Computing section May 10, 2010; accepted for publication (in revised form) April 13, 2011; published electronically July 14, 2011. This work has been partially supported by the Ministerio de Ciencia e Innovacion (Spain) under projects MTM2007-61572 and MTM2010-18246-C03 (cofinanced by the ERDF of the European Union). Additional financial support from the Generalitat Valenciana through project GV/2009/032 (SB), Fundacio Bancaixa (FC), and Universidad del Pais Vasco/Euskal Herriko Uniberstsitatea through project EHU08/43 (AM) is also acknowledged. en_EN
dc.language Inglés es_ES
dc.publisher Society for Industrial and Applied Mathematics es_ES
dc.relation.ispartof SIAM JOURNAL ON SCIENTIFIC COMPUTING es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject error analysis es_ES
dc.subject splitting methods es_ES
dc.subject time dependent Schrodinger equation es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Error analysis of splitting methods for the time dependent Schrodinger equation es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1137/100794535
dc.relation.projectID info:eu-repo/grantAgreement/MEC//MTM2007-61572/ES/ALGORITMOS DE INTEGRACION GEOMETRICA. TEORIA Y APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/Generalitat Valenciana//GV%2F2009%2F032/ES/Desarrollo de integradores geométricos adaptados a ecuaciones diferenciales con diferentes escalas de tiempo/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UPV%2FEHU//EHU08%2F43/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2010-18246-C03-03/ES/TECNICAS ALGEBRAICAS EN INTEGRACION GEOMETRICA/ 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.; Murua, A. (2011). Error analysis of splitting methods for the time dependent Schrodinger equation. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 33(4):1525-1548. https://doi.org/10.1137/100794535 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1137/100794535 es_ES
dc.description.upvformatpinicio 1525 es_ES
dc.description.upvformatpfin 1548 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 33 es_ES
dc.description.issue 4 es_ES
dc.relation.senia 210385
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder European Commission es_ES
dc.contributor.funder Universidad del País Vasco/Euskal Herriko Unibertsitatea es_ES
dc.contributor.funder Fundación Bancaja es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem