The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves

Ostrovsky equation (modified Korteweg–de Vries equation) is used for modeling of a weakly nonlinear surface and internal waves in a rotating ocean. The Ostrovsky equation is a nonlinear partial differential equation and also is complicated due to a nonlinear integral operator as well as spatial and temporal derivatives. In this paper we propose a numerical scheme for solving this equation. Our numerical method is based on a collocation method with three different bases such as BB-spline, Fourier and Chebyshev. A numerical comparison of these schemes is also provided by three examples.