Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review

Analysis, Modeling and Simulation of Multiscale Problems ◽

10.1007/3-540-35657-6_20 ◽

2006 ◽

pp. 553-576 ◽

Author(s):

David Cohen ◽

Tobias Jahnke ◽

Katina Lorenz ◽

Christian Lubich

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Numerical Integrators ◽

Highly Oscillatory

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Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems

IMA Journal of Numerical Analysis ◽

10.1093/imanum/dri020 ◽

2006 ◽

Vol 26 (1) ◽

pp. 34-59 ◽

Author(s):

David Cohen

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Numerical Integrators ◽

Highly Oscillatory

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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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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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Integrators for highly oscillatory Hamiltonian systems: An homogenization approach

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2010.13.347 ◽

2010 ◽

Vol 13 (2) ◽

pp. 347-373 ◽

Author(s):

Claude Le Bris ◽

◽

Frédéric Legoll ◽

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Homogenization Approach ◽

Highly Oscillatory

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Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drs005 ◽

2012 ◽

Vol 33 (1) ◽

pp. 30-56 ◽

Author(s):

M. Dobson ◽

C. Le Bris ◽

F. Legoll

Keyword(s):

Hamiltonian Systems ◽

Constant Frequency ◽

Oscillatory Hamiltonian Systems ◽

Homogenization Approach ◽

Highly Oscillatory ◽

Symplectic Schemes

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Smoothed dynamics of highly oscillatory Hamiltonian systems

Physica D Nonlinear Phenomena ◽

10.1016/0167-2789(95)00212-x ◽

1995 ◽

Vol 89 (1-2) ◽

pp. 28-42 ◽

Author(s):

Sebastian Reich

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Highly Oscillatory

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On Some Difficulties in Integrating Highly Oscillatory Hamiltonian Systems

Computational Molecular Dynamics: Challenges, Methods, Ideas - Lecture Notes in Computational Science and Engineering ◽

10.1007/978-3-642-58360-5_15 ◽

1999 ◽

pp. 281-296 ◽

Author(s):

Uri M. Ascher ◽

Sebastian Reich

Keyword(s):

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Highly Oscillatory

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Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems

Journal of Computational Mathematics ◽

10.4208/jcm.2008-m2018-0218 ◽

2022 ◽

Vol 40 (1) ◽

pp. 70-88

Author(s):

Bin Wang & Xinyuan Wu

Keyword(s):

Energy Conservation ◽

Total Energy ◽

Hamiltonian Systems ◽

Oscillatory Hamiltonian Systems ◽

Long Time ◽

Highly Oscillatory ◽

Oscillatory Energy

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Asymptotic-numerical solvers for highly oscillatory ordinary differential equations and Hamiltonian systems

Computational and Applied Mathematics ◽

10.1007/s40314-021-01675-4 ◽

2021 ◽

Vol 40 (8) ◽

Author(s):

Zhongli Liu ◽

Xiaoxue Sa ◽

Hongjiong Tian

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Hamiltonian Systems ◽

Highly Oscillatory

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