# Article

**Keywords:**

nonlinear water waves; steady waves; wave shoaling; angle of wave breaking; maximum wave height; spectral method

**Summary:**

A Fourier approximation method is used for modeling and simulation of fully nonlinear steady waves. The set of resulting nonlinear equations are solved by Newton's method. The shoaling of waves is simulated based on comparisons with experimental data. The wave heights and the angles of breaking are analysed until the limit of inadequacy of the numerical method. The results appear quite close to those criteria predicted by the theory of completely nonlinear surface waves and contribute to provide information on the study of the relationship between computational modeling and the theory of steady waves.