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

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...

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Autores principales: Auzinger, Winfried, Hofstätter, Harald, Ketcheson, David, Koch, Othmar
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2016
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6407747/
https://www.ncbi.nlm.nih.gov/pubmed/30930704
http://dx.doi.org/10.1007/s10543-016-0626-9
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author Auzinger, Winfried
Hofstätter, Harald
Ketcheson, David
Koch, Othmar
author_facet Auzinger, Winfried
Hofstätter, Harald
Ketcheson, David
Koch, Othmar
author_sort Auzinger, Winfried
collection PubMed
description 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.
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spelling pubmed-64077472019-03-27 Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes Auzinger, Winfried Hofstätter, Harald Ketcheson, David Koch, Othmar BIT Numer Math Article 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. Springer Netherlands 2016-07-28 2017 /pmc/articles/PMC6407747/ /pubmed/30930704 http://dx.doi.org/10.1007/s10543-016-0626-9 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Auzinger, Winfried
Hofstätter, Harald
Ketcheson, David
Koch, Othmar
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
title Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
title_full Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
title_fullStr Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
title_full_unstemmed Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
title_short Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
title_sort practical splitting methods for the adaptive integration of nonlinear evolution equations. part i: construction of optimized schemes and pairs of schemes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6407747/
https://www.ncbi.nlm.nih.gov/pubmed/30930704
http://dx.doi.org/10.1007/s10543-016-0626-9
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