Error Analysis of Nonlinear Simulations: Applications to World Dynamics

Two algorithms for error analysis of nonlinear continuous simulations are derived and presented. A first-order algorithm is developed initially, and its relationship to standard sensitivity algorithms is indicated. This is followed by the development of a Monte Carlo simulation algorithm. The limitations and computational efficiencies of each are discussed and compared. Both algorithms are developed under the assumptions of uncertainty in the inputs to the model, certainty in the accuracy and adequacy of model structure. Simulation techniques for accommodating situations where the latter assumption is not good are then discussed. Using the Forrester world model [1] as the vehicle of demonstration, the techniques show what maximal amount of error can be tolerated in the inputs in order to retain a given accuracy in the outputs.