Algorithm for numerical solution of the optimal control problem for one hydrodynamics model using the COBYLA method

The article discusses an algorithm for approximate solution of the optimal control problem for a nonlinear mathematical model of wave propagation in shallow water. The mathematical model is based on the IMBq equation or the improved modified Boussinesq equation and the Dirichlet boundary conditions and the Showalter-Sidorov initial conditions. The model under study is related to the Sobolev models, since it is based on a degenerate equation. The proposed algorithm combines the phase space method, the Galerkin method, the Ritz method, the decomposition method and the COBYLA method.