A Numerical DAE Approach for Solving a System Dynamics Problem

A system dynamics model first developed using the software STELLA, which explores the complex behaviour of the financially sustainable management of wastewater distribution infrastructure, was converted here into a system of coupled non-linear differential algebraic equations (DAEs). Each differential equation involved a time derivative on a primary variable specifying the temporal evolution of the system. In addition, algebraic (secondary) equations and variables specified the non-linearity inherent in the system as well as any controls on the primary variables constraining the physical evolution of the system relevant to the problem at hand. While STELLA employed a Runge-Kutta numerical strategy, the numerical DAE method used a fully-explicit scheme combined with a fixed-point iteration to resolve the non-linearity. The Runge-Kutta and numerical DAE solutions deviate markedly when the non-linearity of the system becomes pronounced. We demonstrate point-wise stability of the numerical DAE solution as the timestep is refined.