Symbolic Integration of Dynamical Systems by Collocation Methods

Symbolic computational approaches are desirable for many applications and especially for large complex and nonlinear systems. These approaches work well when (a) the user interface is "symbolized" and (b) the underlying computational algorithms are robust. This paper presents advances in both of these areas and for the specific application of numerical integration of large complex nonlinear systems. We present a method for symbolically defining complex nonlinear systems. The methodology includes a human interface for symbolic manipulations of the system model. The system model is symbolically quadratized. The quadratized model is integrated with a numerical method that belongs to the general class of collocating methods. The presented methodologies are superior to previous approaches by the authors using symbolic manipulations and trapezoidal integration. The methodology is illustrated with example systems including converters with saturable inductors, surge arresters and other complex nonlinear systems. The proposed methodology is compared to previous approaches for the purpose of quantifying the advantages