The application of the Sinc-Collocation approach based on derivative interpolation in numerical oceanography

In this paper, the application of a Sinc-Collocation approach based on first derivative interpolation in numerical oceanography is presented. The specific model of interest involves a hydrodynamic model of wind-driven currents in coastal regions and semi-enclosed seas with depth-dependent vertical eddy viscosity. The model is formulated in two different but equivalent systems; a complex-velocity system and a real-valued coupled system. Even in the presence of singularities that are often present in oceanographic problems involving boundary layers, the Sinc-collocation technique provides exponentially convergent approximations. Moreover, the first derivative interpolation approach which uses Sinc-based integration to approximate the unknown has advantages over the customary Sinc method of interpolating the unknown itself since integration has the effect of damping out numerical errors that are inherently present in numerical approximations. Moreover, the approach presented in this paper preserves the appropriate endpoints behaviors of the Sinc bases, resulting in a highly accurate and computationally efficient method. The accuracy and stability of the proposed method is demonstrated through the solution of several model problems. It is further shown that the proposed approach is more accurate and computationally less expensive than those obtained by the Sinc-Galerkin approach reported in previous studies.