Lyapunov stability of the numerical solution of the Saint-Venant equation

The work is devoted to the study of the stability of the finite difference method for the initial-boundary value problem for the system of Saint-Venant equations. Easily the verifiable practical stability conditions have been obtained. Energy estimates are established for an approximate solution of a discrete initial-boundary value problem. This energy estimate allows us to assert the stability of the finite difference method. The corresponding stability theorem is proved. The discrete Lyapunov function is constructed. An a priori estimate is obtained for the numerical solution of the boundary-value difference problem. This estimate allows us to speak about the exponential stability of the numerical solution.