Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

Winfried Auzinger, Harald Hofstätter, David I. Ketcheson, Othmar Koch

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
Original languageEnglish (US)
Pages (from-to)55-74
Number of pages20
JournalBIT Numerical Mathematics
Volume57
Issue number1
DOIs
StatePublished - Jul 28 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Open access funding provided by Technische Universität Wien. This work was supported
by the Austrian Science Fund (FWF) under Grant P24157-N13, and by the Vienna Science and
Technology Fund (WWTF) under Grant MA-14-002. The computational results presented have been
achieved in part using the Vienna Scientific Cluster (VSC).

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