On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization
arXiv:1905.06019 · doi:10.1016/j.physd.2019.05.002
Abstract
In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and Hamiltonian formulations, well-posedness and existence of solitary-wave solutions) were previously analyzed by the authors in Part I. As a second part of the study, considered here is the construction of geometric schemes for the numerical integration. By using the method of lines, the geometric properties, based on the multi-symplectic and Hamiltonian structures, of different strategies for the spatial and time discretizations are discussed and illustrated.
38 pages, 4 figures, 33 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/