期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 442, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2021.110429
关键词
Energy-preserving exponential integrators; Highly oscillatory systems; Modified differential equations; B-series
资金
- National Natural Science Foundation of China [11801377, 11903022, 11671200]
- Natural Science Foundation of Jiangxi Province [20192BCBL23030, 20192ACBL21053]
- Natural Science Foundation of Jiangsu Province [BK20150934]
- Shangrao Science and Technology Talent Plan [2020K006]
This paper presents a uniform framework to design energy-preserving exponential integrators of arbitrarily high order based on the modifying integrator theory. By finding the truncated modified differential equations, arbitrarily high-order integrators are designed for highly oscillatory systems. A fourth-order energy-preserving exponential integrator is constructed and its stability and convergence are analyzed, showing remarkable superiority over existing integrators for highly oscillatory systems.
Taking into account the limited accuracy of the energy-preserving exponential integrator of order two (Li and Wu, 2016 [29]) for conservative or dissipative systems with highly oscillatory solutions, this paper is devoted to presenting a uniform framework to design energy-preserving exponential integrators of arbitrarily high order based on the modifying integrator theory. To this end, we first show that the second-order energy-preserving exponential integrator is a B-series method. Using the adapted substitution law, we then prove that there exist arbitrary order energy-preserving exponential integrators and show how to design arbitrarily high-order integrators by finding the truncated modified differential equations. As an example, the fourth-order energy-preserving exponential integrator is constructed in detail. The stability and convergence of the proposed integrators are analyzed as well. Finally, numerical experiments are accompanied, including both ODEs and PDEs, and the numerical results demonstrate the remarkable superiority over the existing energy-preserving integrators for highly oscillatory systems in the literature. (C) 2021 Elsevier Inc. All rights reserved.
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