Runge-Kutta-Fehlberg-Reverse Adaptive Solution to Rout Reservoir Flood

A Runge-Kutta-Fehlberg-reverse (RKFR) adaptive numerical algorithm for a first-order nonlinear ordinary differential equation is presented and employed to rout floods through reservoir spillways. The classical Runge-Kutta-Fehlberg (RKF) method ignored the local stability, and in the new method the step length will be further adjusted via a local stability parameter, which measurably reflects the fact as the local truncation error is little enough, the local stability might approximately be characterized by the relative error between the initial dependent variable associated with every step and the feedback which may be calculated using a reverse Runge-Kutta (RK) method. The idea is verified with two distinct types of numerical examples, and the results have been shown to advance greatly the accuracy of numerical solution with comparable computed speed relative to the RKF. Subsequently, the RKFR is coupled with the reservoir flood routing process, and integrated into the flood control decision support system of Huanren-Huilong reservoir group in Hunjiang River basin of Northeast China, and the testing result demonstrates it is more scientific and reliable compared with the RKF and RK.