Research on Error Propagation Law of Flood Routingby Fourth-order Runge - Kutta Method - ZHOU Bin (Renmin Zhujiang)
The fourth-order Runge-Kutta method is one of the commonly used algorithms for solvingordinary differential equations of reservoir flood routing. Studying its error propagation law isof great significance for improving the accuracy of results. The equation of flood routing isexpanded by Taylor formula of multivariate function, and the error equation and error propagationequation of each parameter can be obtained after omitting high-order trace. The results show thatwhen the relative margin of error is the same, the influence of the error of inflow during therising period of reservoir water level is stronger than that of outflow. The influence of theerror of outflow during the drawdown period of reservoir water level is stronger than that ofinflow. The single-step error of water level caused by reservoir surface area has opposite sign inthe rising and drawdown periods of reservoir water level, and tends to zero near the highestreservoir water level. For accumulated errors of reservoir water level, the influence of inflowerror during the rising period of reservoir water level is the most significant, that during thedrawdown period is gradually weakened, while the influence of outflow error is graduallystrengthened.