Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part II. Higher-order methods for linear problems

Winfried Auzinger; Othmar Koch; Othmar Koch; Othmar Koch; Mechthild Thalhammer

doi:10.1016/j.cam.2013.04.043

Titel

Autor*in

Winfried Auzinger

Technische Universität Wien

Othmar Koch

Technische Universität Wien

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

journal article

Sprache

Englisch [eng]

Persistent identifier

phaidra.univie.ac.at/o:423906

DOI

10.1016/j.cam.2013.04.043

Erschienen in

Titel

Journal of Computational and Applied Mathematics

Band