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A maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations

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Abstract

Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation (ADHO) for periodic nonlinear oscillation systems is presented. This Maple package is valid for periodic oscillation systems in rather general, and can automatically deliver the accurate approximations of the frequency ω and the mean of motion δ of a nonlinear periodic oscillator. Based on the homotopy analysis method which is valid even for highly nonlinear problems, this Maple package can give accurate approximate expressions even for nonlinear oscillation systems with strong nonlinearity. Besides, the package is user-friendly: One just needs to input a governing equation and initial conditions, and then gets satisfied analytic approximations in few seconds. Several different types of examples are given in this paper to illustrate the validity of this Maple package. Such kind of package provides us a helpful and easy-to-use tool in science and engineering to analyze periodic nonlinear oscillations. And it is free to download the electronic version of this Maple package from the address “http://numericaltank.sjtu.edu.cn/sjliao.htm” once the paper is published publicly.

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Authors and Affiliations

  1. Department of Computer Science and Technology, East China Normal University, Shanghai, 200241, China

    Yinping Liu

  2. State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China

    Shijun Liao

  3. Department of Computer Science, East China Normal University, Shanghai, 200241, China

    Zhibin Li

Authors
  1. Yinping Liu
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  2. Shijun Liao
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  3. Zhibin Li
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Corresponding author

Correspondence to Yinping Liu.

Additional information

This research is supported by the National Science Foundation of China under Grant No. 11071274.

This paper was recommended for publication by Editor Xiao-Shan GAO.

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Liu, Y., Liao, S. & Li, Z. A maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations. J Syst Sci Complex 25, 594–616 (2012). https://doi.org/10.1007/s11424-012-0043-3

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  • DOI: https://doi.org/10.1007/s11424-012-0043-3

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