First- and second-order accurate implicit difference schemes for the Charney-Obukhov equation

In the present work, first- and second-order accurate implicit difference schemes for the numerical solution of the nonlinear Charney-Obukhov equation are constructed. For each constructed scheme, the approximation error is estimated and the convergence of the iterative process is investigated. On the basis of numerical calculations accomplished by means of these schemes, the propagation of a two-dimensional nonlinear solitary Rossby vortex structure is studied. A comparative analysis of the obtained numerical results is carried out