Lecture D1 (2022-09-15): Introduction to Numerical Simulation of Dynamical Systems, Part 1

In this lecture, we introduce numerical simulation of dynamical systems (coupled ordinary differential equations) within the context of stock-and-flow diagrams for System Dynamics Modeling in strategic thinking. After covering how systems of ODE's capture the underlying "forces" driving change in a system, we review different ways to think about compound interest. This compound interest example motivates "Euler's method" for numerical integration over time. That is, we describe the product of flows and time-step durations as a sort of "interest" earned over each simulation time step ("compounding period" in the bank analogy). We use a bacterial growth example to show how this perspective can let us simulate the (average) growth characteristics of a bacterial population without having to simulate the discrete events where each bacteria reproduces independent of each other bacteria. Overall, this lecture relates the "time step" parameter in tools like Vensim and Insight Maker to calculus-based topics like the definition of the derivative. Furthermore, this lecture uses spreadsheet tools (like Microsoft Excel and Google Sheets) to provide a picture of what goes on inside simulation tools like Vensim and Insight Maker.