Nonlinear Stability Analysis of Area-Preserving Integrators

@article{Skeel2000NonlinearSA,
  title={Nonlinear Stability Analysis of Area-Preserving Integrators},
  author={Robert D. Skeel and K. Srinivas},
  journal={SIAM J. Numerical Analysis},
  year={2000},
  volume={38},
  pages={129-148}
}
Linear stability analysis is inadequate for integrators designed for nondissipative systems such as Hamiltonian systems in which nonlinear effects are often decisive. Mathematical theory exists (KAM theory) for rigorous analysis of small perturbations from equilibria, but it needs to be expressed in a form that is more easily applicable to the study of area-preserving maps. We have pursued this, obtaining a completely rigorous nonlinear stability analysis for elliptic equilibria based on the… CONTINUE READING
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