摘要
这研究由在 Lorenz 非线性的方程使用一条多重精确的途径在机器精确和步尺寸上在非线性的动态系统揭示浮点计算的相关性。论文也为与长期的集成和过去常识别最大的有效计算时间(MECT ) 和最佳的步尺寸(OS ) 的一条新 multiple-precision-based 途径在 Lorenz 系统获得一个真实数字解决方案表明过程。另外，作者介绍怎么在非线性的系统的一些典型盒子中在长期的集成分析舍入错误并且介绍它的近似估计表达式。
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.
关键词
非线性动力系统
数值计算
气候
误差
multiple-precision numerical calculation, round-off error, nonlinear dynamical system
