On the convergence of a coupling successive approximation method for solving Duffing equation

Authors

  • Dao Huy Bich Hanoi University of Science, VNU, Vietnam
  • Nguyen Dang Bich Institute for Building Science and Technology (IBST), Hanoi, Vietnam

DOI:

https://doi.org/10.15625/0866-7136/36/3/4843

Keywords:

General Duffing equation, coupling successive approximation method, convergence, complex valued solution, chaotic solution

Abstract

General Duffing equations occur in many problems of Mechanics and Dynamics. These equations include nonlinear terms of second and third order, their coefficients are finite but not small parameters. For finding analytical approximate solutions of the general Duffing equation the coupling successive approximation method (CSAM) has been proposed by the authors.In the present paper the convergence of mentioned method is proven and a condition relating coefficients of Duffing equation to provide the convergence procedure is formulated. Emphasize that the assumption of small parameters is not used in the proving.Some examples are presented to illustrate the proposed method, particularly exact solutions of some problems are compared with analytical approximate ones found by CSAM.

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Published

22-08-2014

How to Cite

Bich, D. H., & Bich, N. D. (2014). On the convergence of a coupling successive approximation method for solving Duffing equation. Vietnam Journal of Mechanics, 36(3), 185–200. https://doi.org/10.15625/0866-7136/36/3/4843

Issue

Section

Research Paper

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