Modeling of Dynamic Systems: An Innovative Approach

Abstract

Engineers have always been interested in describing the time‐dependent response of physical systems, whether they be the motion of a spring or the biogeochemical state of a wastewater stabilization pond. Because of the complexity of many time‐varying systems, engineers have frequently based their design on steady‐state conditions where all time derivatives are set equal to zero. Accordingly, there is a definite need to improve our understanding of dynamic systems and to allow users to model such systems in an efficient and user‐friendly manner. The purpose of this paper is to describe the application of spreadsheets [e.g., Lotus 1‐2‐3 (tm) & Microsoft Excel(tm)] in modeling the dynamics of systems represented by sets of nonlinear ordinary differential equations. The approach that will be presented is general and can be applied to any system that can be described by a set of NODEs. The use of simulation languages for the solution of more complex problems will also be discussed briefly. While spreadsheets might be limited to systems that can be described by a relatively small set of nonlinear ordinary differential equations, this approach provides attractive, practical and pedagogical benefits. On the other hand, simulation languages are particularly well suited for the analysis of large dynamic systems. Examples taken from the environmental engineering and structural engineering literature serve to illustrate the application of spreadsheets to the simulation of dynamic systems.