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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.

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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.

Peter Görtz. (1970). Backward Error Analysis of Symplectic Integrators for Linear Separable Hamiltonian Systems. Journal of Computational Mathematics. 20 (5). 449-460. doi:
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