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 - <p style="text-align: justify;">Symplecticness, stability, and asymptotic properties of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nystr<span style="font-family: 等线; font-size: 19px;">ö</span>m 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.</p>