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Conservative numerical schemes for the Ostrovsky equation. (English) Zbl 1188.83030
Summary: The Ostrovsky equation describes gravity waves under the influence of Coriolis force. It is known that solutions of this equation conserve the \(L^{2}\) 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.

MSC:
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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