Sensitivity Analysis of a Dynamical System Using C+ +

This article introduces basic principles of first order sensitivity analysis and presents an algorithm that can be used to compute the sensitivity of a dynamical system to a selected parameter. This analysis is performed by extending with sensitivity equations the set of differential equations describing the dynamical system. These additional equations require the evaluation of partial derivatives, and so a technique known as the fable algorithm, which can be used to exactly and automatically compute these derivatives, is described. A C++ class which can be used to implement the table algorithm is presented along with a driver routine for evaluating the output of a model and its sensitivity to a single parameter. The use of this driver routine is illustrated with a specific application from environmental hazards modeling.