Development of an algorithm for calculating stable solutions of the Saint-Venant equation using an upwind implicit difference scheme

The problem of numerical determination Lyapunov-stable (exponential stability) solutions the Saint-Venant equations system has remained open until now. authors this paper previously proposed an implicit upwind difference splitting scheme, but its practical applicability was not indicated there. In paper, is solved successfully, namely, algorithm for calculating developed and implemented using scheme on example Big Almaty Canal (hereinafter BAC). As a result application, it established that: 1) we were able to perform computational calculation water level velocity part BAC (10,000 meters) located in region; 2) values height horizontal are consistent with actual measurements parameters flow BAC; 3) stable; 4) stationary solution (exponentially stable); 5) obtained results (according BAC) show efficiency based according calculated time. Since managed increase grid time step up 0.8 scheme.