Conservative numerical schemes for the Ostrovsky equation

摘要

The Ostrovsky equation describes gravity waves under the influence of Coriolis force. It is known that solutions of this equation conserve the L2 norm and an energy function that is determined non-locally. In this paper we propose four conservative numerical schemes for this equation: a finite difference scheme and a pseudospectral scheme that conserve the norm, and the same types of schemes that conserve the energy. A numerical comparison of these schemes is also provided, which indicates that the energy conservative schemes perform better than the norm conservative schemes.