Stability and Accuracy Analysis for Taylor Series Numerical Method

作     者：赵丽滨 姚振汉 王寿梅 

作者机构：Department of Engineering Mechanics Tsinghua University Beijing 100084 China Solid Mechanics Research Center Beihang University Beijing 100083 China 

出 版 物：《Tsinghua Science and Technology》 (清华大学学报（自然科学版（英文版）)

年 卷 期：2004年第9卷第1期

页      面：51-56页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：structural dynamics time integration Taylor series stability accuracy 

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.