Publications in Scientific Journals:

W. Auzinger, O. Koch, M. Thalhammer:
"Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I. The linear case";
Journal of Computational and Applied Mathematics, 236 (2012), ISBN: 978-3-902627-04-9; 2643 - 2659.

English abstract:
We introduce a defect correction principle for exponential operator splitting methods
applied to time-dependent linear Schrödinger equations and
construct a posteriori local error estimators for the Lie-Trotter and Strang splitting methods.
Under natural commutator bounds on the involved operators we prove asymptotical correctness of
the local error estimators, and along the way recover the known a priori convergence bounds.
Numerical examples illustrate the theoretical local and global error estimates

Linear evolution equations, Time-dependent linear Schrödinger equations, Time integration, Exponential operator splitting methods, Defect correction, A priori local error estimates, A posteriori local error estimates

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Electronic version of the publication:

Related Projects:
Project Head Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen

Created from the Publication Database of the Vienna University of Technology.