Ganji, S.S., Ganji, D.D., Karimpour, S. and Babazadeh, H. (2009) Applications of He’s Homotopy Perturbation Method to Obtain Second-Order Approximations of the Coupled Two-Degree-of-Freedom Systems. International Journal of Nonlinear Sciences and Numerical Simulation, 10, 303-312.
https://doi.org/10.1515/IJNSNS.2009.10.3.305

has been cited by the following article:

• TITLE: The Vibrational Motion of a Dynamical System Using Homotopy Perturbation Technique

  AUTHORS: T. S. Amer, A. A. Galal, Shimaa Elnaggar

  KEYWORDS: Homotopy Technique, Nonlinear Vibration, Lagrange’s Equation, Stability

  JOURNAL NAME: Applied Mathematics, Vol.11 No.11, November 13, 2020

  ABSTRACT: This paper outlines the vibrational motion of a nonlinear system with a spring of linear stiffness. Homotopy perturbation technique (HPT) is used to obtain the asymptotic solution of the governing equation of motion. The numerical solution of this equation is obtained using the fourth order Runge-Kutta method (RKM). The comparison between both solutions reveals high consistency between them which confirms that, the accuracy of the obtained solution using aforementioned perturbation technique. The time history of the attained solution is represented through some plots to reveal the good effect of the different parameters of the considered system on the motion at any instant. The conditions of the stability of the attained solution are presented and discussed.