Research on Error Estimation and Continuous Runge-Kutta Algorithm for Real-time Simulation

摘要

In order to evaluate the error of the Runge-Kutta (RK) algorithm used in real-time simulation and apply it to real-time simulation problems with dense output, based on the ODE45 with maximum stability region and least truncation error, this paper adopts a variable step-size strategies and derives a relative ODE35 RK algorithm (a combination of a third- and fifth-order method) to solve error estimation problem. Further, it is extended as the continuous RK algorithm. Thus it can not only be used for real-time simulation, but also be applied to non-real-time variable step-size simulation.