Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough - ZHOU Bin (Renmin Zhujiang)
Explicit Runge-Kutta method is one of the commonly used algorithms to solve the differential equation of constantly gradually varied flow in open channel, which has been studied and popularized by some domestic scholars in recent years. Studying the stability of explicit Runge-Kutta method to solve the constantly gradually varied flow equation in open channel can further consolidate the foundation of technical popularization. The fourth-order explicit Runge-Kutta equation of constantly gradually varied flow in open channel is expanded by Taylor formula of multivariate function, and the error propagation equation can be obtained after omitting high-order trace and eliminating some items. The error propagation equation shows that when the fourth-order explicit Runge-Kutta method is used to solve the differential equation of constantly gradually varied flow in open trough, the slow flow pattern should be calculated from downstream to upstream, and the rapid flow pattern should be calculated from upstream to downstream, so that the stability can be guaranteed when a sufficiently small length is used for calculation. This conclusion can be further verified by typical calculation, and can be further extended to the general explicit Runge-Kutta method.