A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations  

作　　者：Yilong Liu Achim Fischer Peter Eberhard Baohai Wu 

机构地区：[1]Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Northwestern Polytechnical University [2]Institute of Engineering and Computational Mechanics,University of Stuttgart

出　　处：《Acta Mechanica Sinica》2015年第3期406-415,共10页力学学报（英文版）

基　　金：partially supported by a scholarship from the China Scholarship Council;the German Research Foundation (DFG) for financial support within the Cluster of Excellence in Simulation Technology (EXC 310) at the University of Stuttgart

摘　　要：A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.

关 键 词：Full-discretization method Time delay -Stability Chatter 

分 类 号：O175[理学—数学]