Structure-Preserving Algorithms with Uniform Error Bound and Long-time Energy Conservation for Highly Oscillatory Hamiltonian Systems

Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear systems with highly oscillatory solution, and the blended algorithms inherit and respect the...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 95; no. 3; p. 66
Main Authors: Wang, Bin, Jiang, Yaolin
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2023
Springer Nature B.V
Subjects:
Accuracy
Algorithms
Computational Mathematics and Numerical Analysis
Energy conservation
Errors
Hamiltonian functions
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical functions
Mathematics
Mathematics and Statistics
Methods
Nonlinear systems
Numerical analysis
Numerical methods
Theoretical
65L05
Energy-preserving algorithms
65P10
Long-time conservation
65L70
Highly oscillatory systems
Symplectic algorithms
65L20
Uniform error bound
Nonlinear Hamiltonian systems
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear systems with highly oscillatory solution, and the blended algorithms inherit and respect the advantage of each method. Two kinds of algorithms are presented to preserve the symplecticity and energy of the Hamiltonian systems, respectively. Long time energy conservation is analysed for symplectic algorithms and the proposed algorithms are shown to have uniform error bound in the position for the highly oscillatory structure. Moreover, some methods with uniform error bound in the position and in the velocity are derived and analysed. Two numerical experiments are carried out to support all the theoretical results established in this paper by showing the performance of the blended algorithms.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02178-6