A coupling successive approximation method for solving Duffing equation and its application


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




General Duffing equation, coupling successive approximation method, chaos index, chaotic structures of solutions


The paper proposes an algorithm to solve a general Duffing equation, in which a process of transforming the initial equation to a resulting equation is proposed, and then the coupling successive approximation method is applied to solve the resulting equation. By using this algorithm a special physical factor and complex-valued solutions to the general Duffing equation are revealed. The proposed algorithm does not use any assumption of small parameters in the equation solving. The coupling successive procedure provides an analytic approximated solution in both real-valued or complex-valued solution. The procedure also reveals a formula to evaluate the vibration frequency, \(\varphi\), of the non-linear equation. Since the first approximation solution is in a closed-form, the chaos index of the general Duffing equation and the chaotic characteristics of solutions can be predicted. Some examples are used to illustrate the proposed method. In the case of chaotic solution, the Pointcaré conjecture is used for solution verification. 


Download data is not yet available.


Metrics Loading ...




How to Cite

Bich, D. H., & Bich, N. D. (2014). A coupling successive approximation method for solving Duffing equation and its application. Vietnam Journal of Mechanics, 36(2), 77–93. https://doi.org/10.15625/0866-7136/36/2/4095



Research Article

Most read articles by the same author(s)

1 2 3 4 5 > >>