Comparison of two equivalent multisymplectic numerical methods for nonlinear wave equations

Abstract

We consider the nonlinear wave equations in four-dimensional mutisymplectic formulation. The two equivalent mutisymplectic numerical methods are used to do the numerical comparison: one is the multisymplectic box scheme based on four-dimensional multisymplectic formulation; the other is the equivalent method which is derived by eliminating the medium variables from the multisymplectic box scheme. The numerical results show that the first one is more accurate than the second one in computing the local conservative quantities. For the linear wave equation, the local energy and momentum can be preserved up to round error by the first numerical method and we have proved the stability of the two equivalent numerical methods.