| Stability and Accuracy Analysis for Taylor Series Numerical Method |
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| 引用本文： | 赵丽滨 姚振汉 王寿梅. Stability and Accuracy Analysis for Taylor Series Numerical Method[J]. 清华大学学报, 2004, 9(1): 51-56 |
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| 作者姓名： | 赵丽滨 姚振汉 王寿梅 |
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| 作者单位： | [1]DepartmentofEngineeringMechanics,TsinghuaUniversity,Beijing100084,China [2]SolidMechanicsResearchCenter,BeihangUniversity,Beijing100083,China |
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| 摘 要： | The Taylor series numerical method (TSNM) is a time integration method for solving problems in structural dynamics. In this paper, a detailed analysis of the stability behavior and accuracy characteristics of this method is given. It is proven by a spectral decomposition method that TSNM is conditionally stable and belongs to the category of explicit time integration methods. By a similar analysis, the characteristic indicators of time integration methods, the percentage period elongation and the amplitude decay of TSNM, are derived in a closed form. The analysis plays an important role in implementing a procedure for automatic searching and finding convergence radii of TSNM. Finally, a linear single degree of freedom undamped system is analyzed to test the properties of the method.
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| 关 键 词： | 稳定性 精确度 Taylor级数 结构动力学 TSNM 特征指数 |
Stability and Accuracy Analysis for Taylor Series Numerical Method |
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| ZHAO Libin,YAO Zhenhan ),WANG Shoumei. Stability and Accuracy Analysis for Taylor Series Numerical Method[J]. Tsinghua Science and Technology, 2004, 9(1): 51-56 |
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| Authors: | ZHAO Libin YAO Zhenhan ) WANG Shoumei |
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| Affiliation: | ZHAO Libin,YAO Zhenhan ),WANG Shoumei Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China, ?Solid Mechanics Research Center,Beihang University,Beijing 100083,China |
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| Abstract: | The Taylor series numerical method (TSNM) is a time integration method for solving problems in structural dynamics. In this paper, a detailed analysis of the stability behavior and accuracy characteristics of this method is given. It is proven by a spectral decomposition method that TSNM is conditionally stable and belongs to the category of explicit time integration methods. By a similar analysis, the characteristic indicators of time integration methods, the percentage period elongation and the amplitude decay of TSNM, are derived in a closed form. The analysis plays an important role in implementing a procedure for automatic searching and finding convergence radii of TSNM. Finally, a linear single degree of freedom undamped system is analyzed to test the properties of the method. |
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| Keywords: | structural dynamics time integration Taylor series stability accuracy |
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