Finite Volume Methods for Non-Linear Equations

We consider the classical numerical-type of models.  In the first part we deal with finite difference numerical model for irotational water waves. Finite volume methods are based on the integral form. A numerical model for solving the two-dimensional equations is presented. The standard Galerkin method with mixed interpolation is applied. In the second part we consider the water wave equation with a logarithmic nonlinearity. Using the Galerkin method, we establish the existence of solutions of the problem.