Computationally Efficient Simulations of Stochastically Perturbed Nonlinear Dynamical Systems

Abstract

Abstract A probabilistic approach is needed to address systems with uncertainties arising in natural processes and engineering applications. For computational convenience, however, the stochastic effects are often ignored. Thus, numerical integration routines for stochastic dynamical systems are rudimentary compared to those for the deterministic case. In this work, the authors present a method to carry out stochastic simulations by using methods developed for the deterministic case. Thereby, the well-developed numerical integration routines developed for deterministic systems become available for studies of stochastic systems. The convergence of the developed method is shown and the method's performance is demonstrated through illustrative examples.