A new family of real-time redictor-corrector integration algorithms

Abstract

This paper describes a variation of the conventional two-pass explicit Adams- Moulton predictor-corrector integration methods which is suitable for real-time simulation. In this new method the first pass through the state equations uses an Adams-Bash forth type of predictor algo rithm to campute an estimate of the state at the n+1/2 frame instead of the n+1 frame, as is customary. This estimate is then used to compute the derivative at the n+1/2 frame which, along with derivatives at the n, n-1, n-2, ... frames is used in the final corrector pass to calculate the state at the n+1 frame. Unlike conventional two-pass Adams- Moulton methods, these new versions are compatible with real-time inputs. The paper shows that they are also superior based on dynamic accuracy measures and stability measures. A three-pass predictor-corrector integration algorithm compatible with real- time inputs is also presented and shown to yield significantly more accurate results than 3rd-order RK (Runge-Kutta) integra tion.