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Title
Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions
AuthorAuzinger, Winfried In der Gemeinsamen Normdatei der DNB nachschlagen ; Koch, Othmar In der Gemeinsamen Normdatei der DNB nachschlagen ; Quell, Michael
Published in
Numerical algorithms, 2016,, page 1-23
Published2016
Edition
Published version
LanguageEnglish
Document typeJournal Article
Keywords (EN)Nonlinear evolution equations / Splitting methods / Adaptive time integration / Local error / Convergence
URNurn:nbn:at:at-ubtuw:3-2830 Persistent Identifier (URN)
DOI10.1007/s11075-016-0206-8 
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 The work is publicly available
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Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions [1.14 mb]
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Abstract (English)

We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several applications generating intricate patterns and displaying nonsmooth solution dynamics. First, we give a general error analysis for splitting methods for parabolic problems under periodic boundary conditions and derive the necessary smoothness requirements on the exact solution in particular for the GrayScott equation and the Van der Pol equation. Numerical examples demonstrate the convergence of the methods and serve to compare the efficiency of different time-adaptive splitting schemes and of splitting into either two or three operators, based on appropriately constructed a posteriori local error estimators.

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CC-BY-License (4.0)Creative Commons Attribution 4.0 International License