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A modified highly precise direct integration method for a class of linear time-varying systems

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Abstract

It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering applications. For a class of systems, whose coefficients matrix is based on time-varying polynomial, a modified highly precise direct integration (VHPD-T method) was presented. Through introducing new variables and expanding dimensions, the system can be transformed into a time-invariant system, in which the transfer matrix can be computed for once and used forever with a highly precise direct integration method. The method attains higher precision than the common methods (e.g. RK4 and power series) and high efficiency in computation. Some numerical examples demonstrate the validity and efficiency of the method proposed.

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References

  1. Maude R. Mathematical Analysis. London: Edward Arnold, 1986. 170–200

    MATH  Google Scholar 

  2. Zhong W X. On precise time-integration method for structural dynamics (in Chinese). J Dalian Univ Tech, 1994, 34: 131–136

    MATH  MathSciNet  Google Scholar 

  3. Zhong W X. The precise integration for matrix Riccati equations (in Chinese). Comput Struct Mech Appl, 1994, 11: 113–119

    Google Scholar 

  4. Zhong W X. Precise computation for transient analysis (in Chinese). J Comput Struct Mech Appl, 1995, 12: 1–6

    Google Scholar 

  5. Lin J H, Shen W P, Williams F W. A high precision direct integration scheme for structures subjected to transient dynamic loading. Comput Struct, 1995, 56: 113–120

    Article  MATH  MathSciNet  Google Scholar 

  6. Zhou G, Wang Y X, Jia G Q, et al. A homogenized high precise direct integration based on Taylor series. J Shanghai Jiaotong Univ, 2001, 35: 1916–1919

    MATH  Google Scholar 

  7. Wang Y X, Tian X D, Zhou G. Homogenized high precision direct integration scheme and its application in engineering. Commun Numer Methods Eng, 2002, 18: 429–439

    Article  MATH  Google Scholar 

  8. Gu Y X, Chen B S, Zhang H W, et al. Precise time-integration method with dimensional expanding for structural dynamic equations. AIAA J, 2001, 39: 2394–2399

    Article  ADS  Google Scholar 

  9. Tan S J, Zhong W X. Numerical solution of differential Riccati equation with variable coefficients via symplectic conservative perturbation method (in Chinese). J Dalian Univ Tech, 2006, 46: S7–S13

    Google Scholar 

  10. Fu M H, Lan L H, Lu K L, et al. The high order multiplication perturbation method for time-varying dynamic system (in Chinese). Sci Sin-Phys Mech Astron, 2012, 42: 185–191

    Article  Google Scholar 

  11. Zhou G, Jiang L. A high precision direct integration method for periodically time-varying linear system (in Chinese). J Shanghai Jiaotong Univ, 2005, 39: 1016–1019

    MATH  MathSciNet  Google Scholar 

  12. Bathe K J. Finite Element Procedures. Englewood Cliffs: Prentice-Hall, 1982. 12–126

    Google Scholar 

  13. Jiang C S. Linear System Theory and Design. Beijing: Science Press, 2008. 200–203

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    XiaoMei Liu, YongHong Wang & ShiLie Weng

  2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Gang Zhou, Shuai Zhu & WeiRong Sun

Authors
  1. XiaoMei Liu
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  2. Gang Zhou
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  3. Shuai Zhu
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  4. YongHong Wang
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  5. WeiRong Sun
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  6. ShiLie Weng
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Correspondence to XiaoMei Liu.

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Liu, X., Zhou, G., Zhu, S. et al. A modified highly precise direct integration method for a class of linear time-varying systems. Sci. China Phys. Mech. Astron. 57, 1382–1389 (2014). https://doi.org/10.1007/s11433-013-5289-9

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  • DOI: https://doi.org/10.1007/s11433-013-5289-9

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