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Popov, I.P. (1956) A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russian). Doklady Akademii USSR, 3, 308-310.

has been cited by the following article:

• TITLE: Asymptotic Solutions for the Fifth Order Critically Damped Nonlinear Systems in the Case for Small Equal Eigenvalues

  AUTHORS: Md. Firoj Alam, M. Abul Kawser, Md. Mahafujur Rahaman

  KEYWORDS: KBM, Eigenvalues, Critically Damped System, Nonlinearity, Asymptotic Solution, Runge-Kutta Method

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.5 No.4, December 2, 2015

  ABSTRACT: This article examines a fifth order critically damped nonlinearsystem in the case of small equal eigenvalues and tries to find out an asymptotic solution. This paper suggests that the solutions obtained by the perturbation techniques based on modified Krylov-Bogoliubov-Mitropoloskii (KBM) method is consistent with the numerical solutions obtained by the fourth order Runge-Kutta method.