A New Multi-Symplectic Scheme for Nonlinear "Good" Boussinesq Equation (Journal of Computational Mathematics, 2021)
The Hamiltonian formulations of the linear "good" Boussinesq (L.G.B.) equationn and the multi-symplectic formulation of the nonlinear "good" Boussinesq (N.G.B.) equation are considered. For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissmann integrator is derived. We also present numerical experiments, which show that the symplectic and multi-symplectic schemes have excellent long-time numerical behavior.
Keywords: Nonlinear "good" Boussinesq equation; Multi-symplectic; Preissmann integrator; Conservation law.