| 数值积分过程中截断误差和舍入误差的分离方法及其效果检验 |
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| 引用本文： | 王鹏飞,黄荣辉,李建平.数值积分过程中截断误差和舍入误差的分离方法及其效果检验[J].大气科学,2011,35(3):403-410. |
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| 作者姓名： | 王鹏飞 黄荣辉 李建平 |
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| 作者单位： | 1.中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室, 北京,100029;中国科学院研究生院, 北京,100049 |
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| 基金项目： | 国家自然科学基金资助项目40730952， 国家重点基础研究发展计划项目2009CB421405、 2011CB309704 |
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| 摘 要： | 本文讨论数值积分过程中截断误差和舍入误差的分离方法和理论,解析地给出某些数值计算方法的理论截断误差,并以此来分离计算结果中的误差.然后引入参考解的办法,用来分离更为一般的微分方程求解过程中的截断误差和舍入误差.以参考解算法为基础,对一个偏微分方程的数值解进行计算,所得结果与采用理论截断误差得到的结果进行了对比,发现:(...
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| 关 键 词： | 数值积分 截断误差 舍入误差 参考解 |
Separation of Truncation Error and Round-off Error in the Numerical Integration and Its Validation |
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| Wang Pengfei,Huang Ronghui and Li Jianping.Separation of Truncation Error and Round-off Error in the Numerical Integration and Its Validation[J].Chinese Journal of Atmospheric Sciences,2011,35(3):403-410. |
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| Authors: | Wang Pengfei Huang Ronghui and Li Jianping |
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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; Graduate University of Chinese Academy of Sciences, Beijing, 100049;Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100190;State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing,100029 |
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| Abstract: | The authors propose a method to separate the truncation error and the round-off error from the numerical solution.The analytical truncation error formulas of a partial differential equation are given for the upstream scheme and the centered difference scheme,respectively.The reference solution method is then introduced to separate these two types of errors for more general equations.A scheme based on the reference solution is used to obtain the approximate truncation error.Comparing the results for the upstream scheme and the centered difference scheme,the authors find that:1) the approximate truncation error is highly consistent with the analytical one.2) The truncation errors of 1-D wave equations for the two schemes both show wavy periodicities with amplitudes being related to the parameters of computation.3) The analytical error is suitable for the analysis of any slice of t,while the approximate one is only suitable for the analysis of a certain time range.However,the approximate error can be more easily obtained for general differential equations without a complex theoretical deduction. |
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| Keywords: | numerical integration truncation error round-off error reference solution |
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