A review of numerical methods for digital simulation

Abstract

This review is based on an extended study of the litera ture and experience in the detailed simulation of guided missiles and similar systems. After a brief recapitulation of the main ideas behind the classical methods for numer ically solving ordinary differential equations, the recent literature on this subject is surveyed and discussed. Pre dictor, predictor-corrector, and Runge-Kutta methods of various orders are then compared experimentally and theoretically. The theoretical comparison is based on the performance in computing the steady-state frequency response of linearized systems and includes consideration of accuracy, numerical stability, recovery of continuous outputs from sampled outputs, and computing time per step. The factors determining the optimum order are brought out. Other procedures such as different step lengths in different parts of the problem, special-purpose difference equations for "stiff" linear sections of the prob lem, and procedures for inserting wideband noise are dis cussed. The methods currently in use with a number of simulation languages are then summarized, and it is found that there is little consensus on "best" methods. It is concluded that further development is needed of meth ods for handling (a) stiff equations, including the non linear case, (b) mixed step lengths, (c) noise insertion, (d) discontinuities, and (e) recovery of continuous out puts. A list of 75 references is given.