A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We showâ€¦ (More)

Backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods. This is true in particular for the integration of Hamiltonian systemsâ€¦ (More)

Simulations of the dynamics of biomolecules have been greatly accelerated by the use of multiple time-stepping methods, such as the Verlet-I/r-RESPA ~reversible reference system propagatorâ€¦ (More)

A useful method for understanding discretization error in the numerical solution of ODEs is to compare the system of ODEs with the modified equations obtained through backward error analysis, andâ€¦ (More)

The (implicit) midpoint scheme, like higher order Gauss-collocation schemes, is algebraically stable and symplectic, and it preserves quadratic integral invariants. It may appear particularlyâ€¦ (More)

In this paper, we generalize a result by Rubin and Ungar on Hamiltonian systems with a strong constraining potential to thermally embedded systems, i.e. to Langevin dynamics. Such highly oscillatoryâ€¦ (More)

Recent work reported in the literature suggests that for the long-term integration of Hamiltonian dynamical systems one should use methods that preserve the symplectic structure of the ow. In thisâ€¦ (More)

The problem of an ensemble Kalman filter when only partial observations are available is considered. In particular, the situation is investigated where the observational space consists of variablesâ€¦ (More)

Recent work reported in the literature suggest that for the long-term integration of Hamil-tonian dynamical systems one should use methods that preserve the symplectic structure of the ow. This hasâ€¦ (More)

The Hamiltonian particle-mesh (HPM) method is generalized to the spherical shallow water equations, utilizing constrained particle dynamics on the sphere and smoothing with Merileesâ€™ double-periodicâ€¦ (More)