大气科学2011，Vol.35Issue(3)：403-410,8.
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
Separation of Truncation Error and Round-off Error in the Numerical Integration and Its Validation
摘要
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.关键词
数值积分/截断误差/舍入误差/参考解Key words
numerical integration/truncation error/round-off error/reference solution分类
天文与地球科学引用本文复制引用
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):403-410,8.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 （）
