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 計算水力學中所求解的是非線性偏微分(積分)方程組,其數值方法的現有數學理論尚不夠充分,嚴格的穩定性分析、誤差估計和收斂性證明等理論工作的發展還跟不上數值模擬方法的進展。