Abstract: We considered the multisymplectic Hamilton system for the linear Boussinesq equations. We applied Runge Kutta Nystrom methods to discreting the multisymplectic scheme, and obtained the discrete multisymplectic conservation law. Then we constructed a new scheme which is equivalent to the RungeKutta Nystrom integral, and derived its stability condition. Finally we presented some numerical experiments which illustrate the validity of the scheme.

Key words: linear Boussinesq equation, RungeKutta Nystrom method, multisymplectic, conservation law, stability