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Titel
Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part II. Higher-order methods for linear problems
Autor*in
Winfried Auzinger
Technische Universität Wien
Autor*in
Othmar Koch
Technische Universität Wien
Autor*in
Othmar Koch
Technische Universität Wien
... show all
Abstract
In this work, defect-based local error estimators for higher-order exponential operator splitting methods are constructed and analyzed in the context of time-dependent linear Schrödinger equations. The technically involved procedure is carried out in detail for a general three-stage third-order splitting method and then extended to the higher-order case. Asymptotical correctness of the a posteriori local error estimator is proven under natural commutator bounds for the involved operators, and along the way the known (non)stiff order conditions and a priori convergence bounds are recovered. The theoretical error estimates for higher-order splitting methods are confirmed by numerical examples for a test problem of Schrödinger type. Further numerical experiments for a test problem of parabolic type complement the investigations.
Stichwort
Linear evolution equationsTime-dependent linear Schrödinger equationsTime integrationHigher-order exponential operator splitting methodsDefect correctionA priori local error estimatesA posteriori local error estimates
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:423906
Erschienen in
Titel
Journal of Computational and Applied Mathematics
Band
255
Seitenanfang
384
Seitenende
403
Verlag
Elsevier BV
Projektnummer
P24157-N13 – Austrian Science Fund (FWF)
Verfügbarkeitsdatum
2016-01-02
Datum der Annahme zur Veröffentlichung
2014-01-01
Zugänglichkeit

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