High modes smoothing of time schemes for nonlinear parabolic PDEs

We here introduce a stabilization process applied to IMEX time schemes for the simulation of nonlinear parabolic PDEs. The new schemes we derived use a decomposition of the signal into low and high frequency components (to which different time schemes are applied) together with a proper damping of t...

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Bibliographic Details
Published inNumerical algorithms
Main Authors Brachet, Matthieu, Chehab, Jean-Paul
Format Journal Article
LanguageEnglish
Published Springer Verlag 10.02.2025
Subjects
Mathematics
Numerical Analysis
Allen-Cahn equations
Swift-Hohenberg equations
stabilization
Parabolic PDEs
scales separations
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ISSN1017-1398
1572-9265
1572-9265
DOI10.1007/s11075-025-02022-y

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Summary:We here introduce a stabilization process applied to IMEX time schemes for the simulation of nonlinear parabolic PDEs. The new schemes we derived use a decomposition of the signal into low and high frequency components (to which different time schemes are applied) together with a proper damping of the high mode components. This approach allows to design new methods, with enhanced stability and limited perturbation of the constituency. We display numerical analysis of the schemes on the accuracy and the stability. The numerical illustrations we give concern Allen-Cahn and Swift-Hohenberg equations, and show the efficiency of our methods. The effect of the present number of frequencies, and of the stabilization is evaluated on both the energy decay and the dynamics of the model.
ISSN:1017-1398
1572-9265
1572-9265
DOI:10.1007/s11075-025-02022-y