摘要
This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.
This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.
基金
This study was supported by the National Key Basic Research and Development Project of China 2004CB418303
the National Natural Science foundation of China under Grant Nos. 40305012 and 40475027
Jiangsu Key Laboratory of Meteorological Disaster KLME0601.
