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Volume 20, Issue 5
Backward Error Analysis of Symplectic Integrators for Linear Separable Hamiltonian Systems

Peter Görtz

J. Comp. Math., 20 (2002), pp. 449-460.

Published online: 2002-10

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  • Abstract

Symplecticness, stability, and asymptotic properties of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nyström methods applied to the simple Hamiltonian system $\dot{p}= -vq, \dot{q}= kp$ are studied. Some new results in connection with P-stability are presented. The main part is focused on backward error analysis. The numerical solution produced by a symplectic method with an appropriate stepsize is the exact solution of a perturbed Hamiltonian system at discrete points. This system is studied in detail and new results are derived. Numerical examples are presented.

  • Keywords

Hamiltonian systems, Backward error analysis, Symplectic integrators.

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-449, author = {Görtz , Peter}, title = {Backward Error Analysis of Symplectic Integrators for Linear Separable Hamiltonian Systems}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {5}, pages = {449--460}, abstract = {

Symplecticness, stability, and asymptotic properties of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nyström methods applied to the simple Hamiltonian system $\dot{p}= -vq, \dot{q}= kp$ are studied. Some new results in connection with P-stability are presented. The main part is focused on backward error analysis. The numerical solution produced by a symplectic method with an appropriate stepsize is the exact solution of a perturbed Hamiltonian system at discrete points. This system is studied in detail and new results are derived. Numerical examples are presented.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8931.html} }
TY - JOUR T1 - Backward Error Analysis of Symplectic Integrators for Linear Separable Hamiltonian Systems AU - Görtz , Peter JO - Journal of Computational Mathematics VL - 5 SP - 449 EP - 460 PY - 2002 DA - 2002/10 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8931.html KW - Hamiltonian systems, Backward error analysis, Symplectic integrators. AB -

Symplecticness, stability, and asymptotic properties of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nyström methods applied to the simple Hamiltonian system $\dot{p}= -vq, \dot{q}= kp$ are studied. Some new results in connection with P-stability are presented. The main part is focused on backward error analysis. The numerical solution produced by a symplectic method with an appropriate stepsize is the exact solution of a perturbed Hamiltonian system at discrete points. This system is studied in detail and new results are derived. Numerical examples are presented.

Görtz , Peter. (2002). Backward Error Analysis of Symplectic Integrators for Linear Separable Hamiltonian Systems. Journal of Computational Mathematics. 20 (5). 449-460. doi:
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