Abstract for: Extending System Dynamics approach to higher index DAE’s

The aim of this paper is to propose an extension of System Dynamics approach for modeling systems to systems described by higher index DAEs (Differential Algebraic Equations). Existing implementations of Forrester’s methodology are commonly based on fixed step integration methods such as Euler or n-order explicit Runge-Kutta. The main reason for using fixed step integration schemes is their simplicity of imple-mentation as well as the the simplicity of modeling environments based on these integration schemes. On the other hand using fixed step integration can lead to incorrect results especially when equations are stiff. The problems with adequate integration schemes can be overcome by using variable stepsize integration methods such BDF or implicit Runge-Kutta. Since these methods require jacobians of right-hand sides of equations these numerical methods must be supported by procedures for evaluating jacobians either by finite difference, or by automatic differentiation (in order to keep the simplicity of modeling environment). Once we have variable stepsize integration procedure we can attempt to extend Forrester’s approach to systems described by fully implicit DAEs – the paper shows how it can be achieved.