The shortcomings of the traditional methods that trial-and-error method, approximate solution and iteration method were used to compute the water surface curves of natural watercourses resulting in large amount of calculations, low precise and complex resolving problems.

After introducing various uncertain factors including a stochastic initial condition,a stochastic coefficient and a stochastic input term into calculating program of flow profiles in river, a stochastic differential equation is established.

Sediment-carrying capacity in natural rivers;

Application of varies increment iteration to simulation of water-surface profile in natural channels;

Astringency and divergency analysis of natural channelsurface line calculation;

Demonstration and application of a mathematical model of unsteady flow in natural channels;

The scheme can be applied to simulating dam -break flood wave propagation in the natural river courses.

The algorithm can be applied to model dam break flood wave propagation in natural river courses or reservoirs.

The main advantage of the scheme stems from the ability to compute the weak solutions of unsteady free-surface flows in the natural river courses and the simplicity.