| Analysis and Application of Multiple-Precision Computation and Round-off Error for Nonlinear Dynamical Systems |
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| 作者姓名： | 王鹏飞 黄刚 王在志 |
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| 作者单位： | [1]State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics （ LASG）, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029 [2]National Climate Center, Beijing 100081 |
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| 基金项目： | 国家重点基础研究发展计划(973计划)，国家自然科学基金，Jiangsu Key Laboratory of Meteorological Disaster KLME0 |
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| 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.
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| 关 键 词： | 非线性动力系统 数值计算 气候 误差 |
| 收稿时间： | 2005-10-08 |
| 修稿时间： | 2006-04-25 |
Analysis and application of multiple-precision computation and round-off error for nonlinear dynamical systems |
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| Pengfei Wang,Gang Huang,Zaizhi Wang.Analysis and Application of Multiple-Precision Computation and Round-off Error for Nonlinear Dynamical Systems[J].Advances in Atmospheric Sciences,2006,23(5):758-766. |
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| Authors: | Pengfei Wang Gang Huang Zaizhi Wang |
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| Institution: | State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,National Climate Center, Beijing 100081 |
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| Abstract: | 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 demonstrates 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. |
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| Keywords: | multiple-precision numerical calculation round-off error nonlinear dynamical system |
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