| Abstract: |
| Symplectic integrators preserve the phase-space volume and have favorable performances in long time simulations. Methods for explicit symplectic integration have been extensively studied for separable Hamiltonians (i.e., H(q,p)=K(p)+V(q)), and they lead to both accuracy and efficiency. However, nonseparable Hamiltonians also model important problems. Unfortunately, implicit methods had been the only available symplectic approach with long-time accuracy for general nonseparable systems. This talk will construct explicit symplectic integrators for nonseparable systems. These new integrators are based on a mechanical restraint that binds two copies of phase space together, and they can be made arbitrarily high-order. Using backward error analysis, KAM theory, and some additional multiscale analysis, a pleasant error bound is established for integrable systems. Numerical evidence of statistical accuracy for non-integrable systems were also observed. |
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