the non-linear partial differential ( integral ) equation often needs to be solved in the computational hydraulics, however, the mathematical theory of its numerical method has yet not been sufficient at present, for example, the development of some theories such as the strict stability analysis, error estimate and convergence proof has been unable to keep pace with the development of the numerical simulation method 计算水力学中所求解的是非线性偏微分(积分)方程组,其数值方法的现有数学理论尚不够充分,严格的稳定性分析、误差估计和收敛性证明等理论工作的发展还跟不上数值模拟方法的进展。