Long-term analysis of symplectic or symmetric extended RKN methods for nonlinear wave equations Article Swipe
Bin Wang
,
Xinyuan Wu
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1805.06679
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1805.06679
This paper analyses the long-time behaviour of one-stage symplectic or symmetric extended Runge--Kutta--Nyström (ERKN) methods when applied to nonlinear wave equations. It is shown that energy, momentum, and all harmonic actions are approximately preserved over a long time for one-stage explicit symplectic or symmetric ERKN methods when applied to nonlinear wave equations via spectral semi-discretisations. For the long-term analysis of symplectic or symmetric ERKN methods, we derive a multi-frequency modulated Fourier expansion of the ERKN method and show three almost-invariants of the modulation system. In the analysis of this paper, we neither assume symmetry for symplectic methods, nor assume symplecticity for symmetric methods. The results for symplectic and symmetric methods are obtained as a byproduct of the above analysis. We also give another proof by establishing a relationship between symplectic and symmetric ERKN methods and trigonometric integrators which have been researched for wave equations in the literature.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1805.06679
- https://arxiv.org/pdf/1805.06679
- OA Status
- green
- Cited By
- 2
- References
- 29
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2894880849
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W2894880849Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1805.06679Digital Object Identifier
- Title
-
Long-term analysis of symplectic or symmetric extended RKN methods for nonlinear wave equationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2018Year of publication
- Publication date
-
2018-05-17Full publication date if available
- Authors
-
Bin Wang, Xinyuan WuList of authors in order
- Landing page
-
https://arxiv.org/abs/1805.06679Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1805.06679Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/1805.06679Direct OA link when available
- Concepts
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Symplectic geometry, Mathematics, Mathematical analysis, Nonlinear system, Mathematical physics, Pure mathematics, Physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
- Citations by year (recent)
-
2021: 1, 2019: 1Per-year citation counts (last 5 years)
- References (count)
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29Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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