Systems of Differential Equations

The next simulation model that I studied was of the Air Land Battle using Lanchester differential equations.  The system of differential equations I developed was more complicated than the simple force-on-force model of the Land Battle.  My model involved three types of forces for each side: multi-role fighter aircraft, air defences and ground forces.  I began by solving the continuous large-scale model using differential equations with the Runge-Kutta method.  Then I developed a discrete small-scale model that I solved probabilistically using a Markov model.  In this work, I realized the parallels between the macro view of continuous models and the micro view of discrete models.  This became useful later when I was comparing System Dynamics models with Agent Based models.