## Smoothed Dynamics of Highly Oscillatory Hamiltonian Systems (1995)

Venue: | Physica D |

Citations: | 17 - 8 self |

### BibTeX

@ARTICLE{Reich95smootheddynamics,

author = {Sebastian Reich},

title = {Smoothed Dynamics of Highly Oscillatory Hamiltonian Systems},

journal = {Physica D},

year = {1995},

volume = {89},

pages = {28--42}

}

### OpenURL

### Abstract

We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step-size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion...