Long-time analysis of extended RKN integrators for Hamiltonian systems with a solution-dependent high frequency Article Swipe
Bin Wang
,
Xinyuan Wu
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1803.07861
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1803.07861
In this paper, we analyse the long-time behaviour of the extended RKN (ERKN) integrators for solving highly oscillatory Hamiltonian systems with a slowly varying, solution-dependent high frequency. We prove that a symmetric ERKN integrator approximately conserves a modified action and a modified total energy over long time intervals based on the technique of varying-frequency modulated Fourier expansion. An illustrative numerical experiment is carried out and the numerical results strongly support the theoretical analysis presented in this paper. As a byproduct of this work, similar long-time behaviour is also investigated for an RKN method.
Related Topics
Concepts
Integrator
Hamiltonian (control theory)
Mathematics
Hamiltonian system
Fourier analysis
Fourier transform
Work (physics)
Frequency analysis
Mathematical analysis
Numerical analysis
Fourier series
Applied mathematics
Control theory (sociology)
Physics
Mathematical optimization
Algorithm
Computer science
Quantum mechanics
Voltage
Control (management)
Artificial intelligence
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1803.07861
- https://arxiv.org/pdf/1803.07861
- OA Status
- green
- Cited By
- 1
- References
- 22
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2792559069
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2792559069Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1803.07861Digital Object Identifier
- Title
-
Long-time analysis of extended RKN integrators for Hamiltonian systems with a solution-dependent high frequencyWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2018Year of publication
- Publication date
-
2018-03-21Full publication date if available
- Authors
-
Bin Wang, Xinyuan WuList of authors in order
- Landing page
-
https://arxiv.org/abs/1803.07861Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1803.07861Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1803.07861Direct OA link when available
- Concepts
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Integrator, Hamiltonian (control theory), Mathematics, Hamiltonian system, Fourier analysis, Fourier transform, Work (physics), Frequency analysis, Mathematical analysis, Numerical analysis, Fourier series, Applied mathematics, Control theory (sociology), Physics, Mathematical optimization, Algorithm, Computer science, Quantum mechanics, Voltage, Control (management), Artificial intelligenceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
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2018: 1Per-year citation counts (last 5 years)
- References (count)
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22Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.conserves | 35 |
| abstract_inverted_index.intervals | 47 |
| abstract_inverted_index.long-time | 6, 84 |
| abstract_inverted_index.modulated | 54 |
| abstract_inverted_index.numerical | 59, 66 |
| abstract_inverted_index.presented | 73 |
| abstract_inverted_index.symmetric | 31 |
| abstract_inverted_index.technique | 51 |
| abstract_inverted_index.expansion. | 56 |
| abstract_inverted_index.experiment | 60 |
| abstract_inverted_index.frequency. | 26 |
| abstract_inverted_index.integrator | 33 |
| abstract_inverted_index.Hamiltonian | 18 |
| abstract_inverted_index.integrators | 13 |
| abstract_inverted_index.oscillatory | 17 |
| abstract_inverted_index.theoretical | 71 |
| abstract_inverted_index.illustrative | 58 |
| abstract_inverted_index.investigated | 88 |
| abstract_inverted_index.approximately | 34 |
| abstract_inverted_index.varying-frequency | 53 |
| abstract_inverted_index.solution-dependent | 24 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/7 |
| sustainable_development_goals[0].score | 0.8600000143051147 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile |