Contributions to Books:

W. Auzinger, O. Koch, M. Thalhammer:
"Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I. The linear case";
in: "ASC Report 34/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

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

Electronic version of the publication:

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