The method of manufactured solutions applied to chaotic systems

In this paper, the method of manufactured solutions is applied to dynamical systems possessing chaotic behavior. This method is used in a non-traditional way to identify points with potential numerical errors and to improve computational efficiency. The numerical errors may be due to the selection of error tolerances in the integration of the ordinary differential equations, computer arithmetic precision, etc. Two classical chaotic models and two ship capsize models are examined. The current approach has similarities to entrainment methods in chaotic control theory, where entrainment refers to two dynamical systems having the same period, phase and amplitude. The convergent region from control theory is used to give a rough guide for identifying potentially catastrophic numerical errors for the classical chaotic models. The effectiveness of this method in improving computational efficiency is demonstrated for the ship capsize models.