Arbitrary-order exponential energy-preserving collocation methods for solving conservative or dissipative systems Article Swipe
In this paper, we present and analyse a novel class of exponential energy-preserving collocation methods for solving conservative or dissipative systems based on exponential integrators and finite element methods. It is shown that these novel methods can be of arbitrarily high order and preserve first integrals or Lyapunov functions. We also consider order estimates and effective implementations of the new methods. Furthermore, we explore and discuss the application of our methods in important stiff gradient systems, and it turns out that our methods are unconditionally energy-diminishing and strongly damped even for very stiff gradient systems. Practical examples of the new methods are derived and the efficiency and superiority are confirmed and demonstrated by three numerical experiments including a nonlinear Schr\{o}dinger equation. As a byproduct of this paper, arbitrary-order trigonometric/RKN energy-preserving collocation methods are presented and analysed for second-order highly oscillatory/general systems.
Related Topics
Concepts
Dissipative system
Collocation (remote sensing)
Exponential function
Trigonometry
Applied mathematics
Mathematics
Collocation method
Energy (signal processing)
Lyapunov function
Nonlinear system
Mathematical analysis
Computer science
Ordinary differential equation
Differential equation
Physics
Machine learning
Quantum mechanics
Statistics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/pdf/1712.07830
- OA Status
- green
- Cited By
- 2
- References
- 41
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2777972145
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2777972145Canonical identifier for this work in OpenAlex
- Title
-
Arbitrary-order exponential energy-preserving collocation methods for solving conservative or dissipative systemsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2017Year of publication
- Publication date
-
2017-12-21Full publication date if available
- Authors
-
Bin Wang, Xinyuan WuList of authors in order
- Landing page
-
https://arxiv.org/pdf/1712.07830Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1712.07830Direct OA link when available
- Concepts
-
Dissipative system, Collocation (remote sensing), Exponential function, Trigonometry, Applied mathematics, Mathematics, Collocation method, Energy (signal processing), Lyapunov function, Nonlinear system, Mathematical analysis, Computer science, Ordinary differential equation, Differential equation, Physics, Machine learning, Quantum mechanics, StatisticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
- Citations by year (recent)
-
2018: 2Per-year citation counts (last 5 years)
- References (count)
-
41Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.oscillatory/general | 139 |
| 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 | 0.8899999856948853 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile |