Chapter 11. The Numerical Step Size

Chapter 3 explains the numerical approach used to generate the simulation results in system dynamics models. You learned that the calculations are repeated over and over as time is advanced in small increments to cover the entire time interval. The time increment is called DT which stands for "delta time." This chapter reviews the previous suggestions and provides additional guidelines for arriving at a suitable value of DT. The most important part of this chapter is the simulations to illustrate what you will see when you have selected a poor value of DT.

Introduction

Recall the Mono Lake simulations that ran from 1990 to 2090. The DT was set to 0.25 years, so the simulation required 400 steps. You learned that we can check the accuracy of the numerical results by cutting DT in half and repeating the simulation. The computer would then need 800 steps to complete the simulation. If we get essentially the same results with 800 steps as with 400 steps, we can be confident that the original results are numerically accurate.

At this point in the book, you have seen models of populations, bank balances, water flows, flowered areas and widget sales. How is it possible that we have come this far without discussing additional guidelines for DT? The answer, quite simply, is that 0.25 time units turns out to be a remarkably good starting value. Each new situation has its own time horizon, but the software gives us the opportunity to describe the units of time to fit our situation. When working with Mono Lake, we chose "years." A DT of 0.25 years means that 400 steps were needed to complete the 100-year simulation. When working with the two bottles exercise in Appendix C, we chose "seconds" and used the model to simulate the fluid flows over an 80-second interval. The computer used 320 steps to complete the simulation. In both cases, we obtained fast and accurate simulations without worrying about the choice of DT.

Not every situation will be as simple as the previous examples, so it is time to take a closer look at the selection of DT. Some additional guidelines are needed to help ensure that our first guess at DT is reasonable.