The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications

Journal of Computational Physics ◽

10.1016/j.jcp.2016.07.033 ◽

2016 ◽

Vol 323 ◽

pp. 171-190 ◽

Author(s):

Lijie Mei ◽

Xinyuan Wu

Keyword(s):

Group Theory ◽

Hamiltonian Systems ◽

Arbitrary Order ◽

Oscillatory Hamiltonian Systems ◽

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Highly Accurate Explicit Symplectic ERKN Methods for Multi-frequency Oscillatory Hamiltonian Systems

Structure-Preserving Algorithms for Oscillatory Differential Equations II ◽

10.1007/978-3-662-48156-1_9 ◽

2015 ◽

pp. 193-209

Author(s):

Xinyuan Wu ◽

Kai Liu ◽

Wei Shi

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

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Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems

Computer Physics Communications ◽

10.1016/j.cpc.2011.09.002 ◽

2012 ◽

Vol 183 (1) ◽

pp. 86-98 ◽

Author(s):

Zhaoxia Chen ◽

Xiong You ◽

Wei Shi ◽

Zhongli Liu

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

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A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems

BIT Numerical Mathematics ◽

10.1007/s10543-021-00846-3 ◽

2021 ◽

Author(s):

Bin Wang ◽

Xinyuan Wu

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Highly Oscillatory

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Efficient Energy-Preserving Integrators for Multi-frequency Oscillatory Hamiltonian Systems

Structure-Preserving Algorithms for Oscillatory Differential Equations II ◽

10.1007/978-3-662-48156-1_4 ◽

2015 ◽

pp. 69-93

Author(s):

Xinyuan Wu ◽

Kai Liu ◽

Wei Shi

Keyword(s):

Hamiltonian Systems ◽

Efficient Energy ◽

Oscillatory Hamiltonian Systems

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High-Order Symplectic and Symmetric Composition Methods for Multi-Frequency and Multi-Dimensional Oscillatory Hamiltonian Systems

Journal of Computational Mathematics ◽

10.4208/jcm.1502-m2014-0082 ◽

2015 ◽

Vol 33 (4) ◽

pp. 356-378 ◽

Author(s):

Kai Liu and Xinyuan Wu

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Composition Methods

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Diagonal implicit symplectic extended RKN methods for solving oscillatory Hamiltonian systems

Computational and Applied Mathematics ◽

10.1007/s40314-019-0786-8 ◽

2019 ◽

Vol 38 (1) ◽

Author(s):

Mingxue Shi ◽

Hao Zhang ◽

Bin Wang

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems

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Efficient energy-preserving integrators for oscillatory Hamiltonian systems

Journal of Computational Physics ◽

10.1016/j.jcp.2012.10.015 ◽

2013 ◽

Vol 235 ◽

pp. 587-605 ◽

Author(s):

Xinyuan Wu ◽

Bin Wang ◽

Wei Shi

Keyword(s):

Hamiltonian Systems ◽

Efficient Energy ◽

Oscillatory Hamiltonian Systems

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Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions

BIT Numerical Mathematics ◽

10.1007/s10543-014-0527-8 ◽

2014 ◽

Vol 55 (3) ◽

pp. 705-732 ◽

Author(s):

David Cohen ◽

Ludwig Gauckler ◽

Ernst Hairer ◽

Christian Lubich

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Numerical Integrators ◽

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Symplectic schemes for highly oscillatory Hamiltonian systems with varying fast frequencies

Comptes Rendus Mathematique ◽

10.1016/j.crma.2010.08.005 ◽

2010 ◽

Vol 348 (17-18) ◽

pp. 1033-1038

Author(s):

Matthew Dobson ◽

Claude Le Bris ◽

Frédéric Legoll

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Highly Oscillatory ◽

Symplectic Schemes

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Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems of arbitrary order

Journal of the London Mathematical Society ◽

10.1112/jlms/jdq079 ◽

2011 ◽

Vol 84 (1) ◽

pp. 159-182

Author(s):

M. Muzzulini

Keyword(s):

Hamiltonian Systems ◽

Arbitrary Order ◽

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