A Nonlinear Galerkin Method for the Shallow-Water Equations on Periodic Domains

A nonlinear Galerkin method for the shallow-water equations is developed, based on spectral transforms. The scheme is compared to a pseudo-spectral Galerkin method. Our numerical results indicate that the nonlinear scheme has the potential advantage of providing similar accuracy at a lower cost than the Galerkin method. The nonlinear method has also less restrictive stability conditions.