Homotopy perturbation method coupled with the enhanced perturbation method

Xiao Xia Li, Chun Hui He*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

81 Citations (Scopus)


The enhanced perturbation method is used to improve a governing equation to a higher order, followed by the classic perturbation method. This paper adopts the basic idea of the method to construct a homotopy equation with a higher order. The results show that this modification of the homotopy perturbation method leads to a very high accuracy of the obtained solution. Its solution process is elucidated by using Duffing oscillator as an example, and the obtained frequency is valid for all amplitudes from an extremely small value to infinity with a maximal error of 3.34%. The main merit of this higher order homotopy perturbation method is that the obtained frequency is valid for the whole solution domain.

Original languageEnglish
Pages (from-to)1399-1403
Number of pages5
JournalJournal of Low Frequency Noise Vibration and Active Control
Issue number3-4
Publication statusPublished - 1 Dec 2019
Externally publishedYes


  • Duffing equation
  • frequency–amplitude relation
  • Homotopy perturbation method
  • periodic solution


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