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 引用本文: 邢誉峰 杨蓉. 单步辛算法的相位误差分析及修正[J]. 力学学报, 2007, 23(5): 668-671.
Yufeng Xing, Rong Yang. Phase errors and their correction in symplectic implicit single-step algorithm[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 668-671.
 Citation: Yufeng Xing, Rong Yang. Phase errors and their correction in symplectic implicit single-step algorithm[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 668-671.

## Phase errors and their correction in symplectic implicit single-step algorithm

• 摘要: 若一个算法的幅值误差和相位误差都不累加，则该算法就是最理想的算法，但这样的算法难以构造. 辛几何算法解决了幅值误差的累加问题，但相位误差累加问题仍然存在. 给出了单步隐式辛算法相位误差的精确估计公式，提出了简单而实用的修正方法. 以Euler中点隐式辛差分格式为例，针对几个线性动力学系统，对相位误差进行了数值分析和修正.

Abstract: For dynamic systems, an algorithm without theaccumulation of phase errors and magnitude errors isideal, but not easy to be found. Although there is no accumulation ofmagnitudes errors in Symplecticdifference algorithms, but the phase errors do accumulate. In this paper, thephase errors of single-step implicit symplectic algorithms, such assymplectic RK algorithms, are analyzed for linear systems withdamping and without damping, and the correction technique is proposed, which issimple and practical. The Euler implicit midpoint integration algorithm isadopted to solve several linear problems, and the results show that thecorrection technique of phase errors is valid. It is concludedthat the phase error is directly related to the quantity h\omega ,which is the product of time step and frequency. The higher the frequency,the higher the phase error; and it is hard to control the phaseerrors for MDOF systems.

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