Computer simulation of rapidly responding forced exponential systems

Abstract

Two common problems in computer simulations are the decisions to ignore or include a particular element of a system under study in a model and the choice of an appropriate integration algorithm. To examine aspects of these problems, a simple exponential system is considered in which a large simulation error is induced by a rather small truncation error. The effect of computational precision, step size and hardware selection on this error is examined at standard and extended precisions over a range of step sizes and on a variety of computers. For this model, simulation accuracy is an exponential function of the number of bits in the mantissa of the computer word. Optimal step size is a function of accuracy required and precision used; a trade-off between truncation and round-off errors becomes important as accuracy requirements increase. Machine selection is important primarily in economic terms if the required precision is available. We conclude that the effect on a simulation of small terms such as truncation errors can be unexpectedly large, that solutions should always be checked, and that high precision and wide dynamic range are important to the successful computer simulation of models such as that examined.