26The Chebyshev spectral collocation method is presented in detail and applied to a reduced gravity ocean model of a rectangular closed basin. As a model problem we solve the propagation of equatorial Kelvin waves which are converted into equatorial Rossby waves and coastal Kelvin waves upon reflection. The solutions obtained by the collocation method are compared with finite difference solutions solved on an Arakawa C-grid. We find that, for similar accuracy, the collocation method requires only 15% of the storage needed by the finite difference method, while the computer time differs by less than 20%.