Multisymplectic structure and multisymplectic scheme for the nonlinear wave equation (Q1611094)

The study of symplectic schemes has achieved great success in the last two decades. Recently there has been ever growing the interest of research and realization underlining multisymplectic properties of partial differential equations, which have multisymplectic Hamiltonian forms. In this paper the multisymplectic structure of the nonlinear wave equation is derived from the variational principle. For numerical calculations, a multisymplectic nine points scheme is presented, which is equivalent to the multisymplectic Preissman scheme. A series of numerical results is given which illustrate the effectiveness of this scheme.