Numerical study of an equation related to wave propagation

We discuss two algorithms for the computation of approximate solutions of a generalization of the so-called Benjamin-Bona-Mahony equation, which is a model proposed to describe unidirectional propagation of long water waves. Both schemes discussed are quadratically convergent with respect to Δt in theH ¹-norm. They use the Galerkin method for the space variable in such a way that the global truncation error has the same order as the error for the interpolation with the Galerkin basis. Estimates are obtained for the study of the discretization that also yield an existence proof for the exact problem. Results of some numerical experiments are presented.