Journal of East China Normal University(Natural Sc ›› 2018, Vol. 2018 ›› Issue (4): 129-137.doi: 10.3969/j.issn.1000-5641.2018.04.013

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A study of approximate analytical solutions of a kind of typical second-order nonlinear different equation

LOU Zhi-mei1, WANG Yuan-bin2, WANG Peng3   

  1. 1. Department of Physics, Shaoxing University, Shaoxing Zhejiang 312000, China;
    2. Department of Mathematics, Shaoxing University, Shaoxing Zhejiang 312000, China;
    3. School of Civil Engineering and Architecture, University of Jinan, Jinan 250022, China
  • Received:2017-07-26 Online:2018-07-25 Published:2018-07-19

Abstract: In a non-inertial rotational reference frame, the motion of a system can be governed by a kind of second-order nonlinear differential equation, in which the numerator and denominator both contain nonlinear terms; in this context, it is hard to obtain an approximate solution for this strongly nonlinear equation. In this paper, we study the approximate solution of the second-order nonlinear differential equation by the Adomian decomposition method. Comparisons between the approximate solution and the numerical solution by using two other methods are also made. The results show that, in the first quarter period, the approximate solutions obtained by the Adomian decomposition method is in good agreement with the numerical solutions and the error of the approximate solutions are smaller than the other solutions obtained by the homotopy asymptotic method.

Key words: Adomian decomposition method, second order nonlinear differential equation, approximate analytical solution, numerical solution

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