An optimal control problem when modeling the rectification process in the column is considered. The process is described by a system of first-order hyperbolic equations with dynamic boundary conditions. A specific peculiarity of the model under consideration is in the boundary conditions of a special type. At each of the boundaries, boundary conditions are determined from a system of ordinary differential equations, which also includes unknown values of functions on another boundary. Three variants of numerical methods for solving the considered problem are proposed. The first method is based on a linearized maximum principle. Structurally it coincides with a conditional gradient method in a corresponding functional space. The second method is a modification of a two-parameter maximum principle method. This method makes it possible to work effectively with internal admissible controls in contrast to standard iterative maximum principle methods. The third method is based on the procedure of discretization of the problem and the use of the standard SciPy Python library to solve the corresponding mathematical programming problem. The results of numerical experiments are illustrated by a series of tables and graphs. As a result, the conditional gradient method may be recommended for solving the problem under consideration.