On the numerical stability for some symplectic integrators

Details On the numerical stability for some symplectic integrators On the numerical stability for some symplectic integrators

Oct 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006acasn..47..418l&link_type=abstract

Acta Astronomica Sinica, vol. 47, no. 4, p.418-431

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Celestial Mechanics: Symplectic Integrator, Linear Stability

Scientific paper

This research deals mainly with an analysis of the linear stability of several symplectic integrators for a linear Hamiltonian system, which involve the first-order implicit symplectic Euler scheme, the second-order implicit centered Euler difference scheme, the first-order explicit symplectic Euler scheme and the second-order explicit leapfrog symplectic integrator. Meantime, a stable region for each integrator is found. The fact is also checked by numerical tests. Especially for a system with a real symmetric quadratic form, a simpler way to study the numerical stability is to use diagonalizing transformations. As an emphasis, a rather larger stable time step of each algorithm is admissible for either a linear or nonlinear system with integrable separations of one main piece and another petty piece rather than a kinetic energy and a potential energy.

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