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Acta Mechanica Sinica

, Volume 31, Issue 3, pp 406–415 | Cite as

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

  • Yilong LiuEmail author
  • Achim Fischer
  • Peter Eberhard
  • Baohai Wu
Research Paper

Abstract

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.

Keywords

Full-discretization method Time delay Stability  Chatter 

Notes

Acknowledgments

This project was partially supported by a scholarship from the China Scholarship Council while Y.L. was visiting the University of Stuttgart. A.F. and P.E. would like to thank the German Research Foundation (DFG) for financial support within the Cluster of Excellence in Simulation Technology (EXC 310) at the University of Stuttgart.

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Yilong Liu
    • 1
    Email author
  • Achim Fischer
    • 2
  • Peter Eberhard
    • 2
  • Baohai Wu
    • 1
  1. 1.Key Laboratory of Contemporary Design and Integrated Manufacturing TechnologyNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Institute of Engineering and Computational MechanicsUniversity of StuttgartStuttgartGermany

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