Asymptotic Solutions of Fifth Order Overdamped-Oscillatory Nonlinear Systems

  • Harun-Or-Roshid Department of Mathematics, Pabna Science and Technology University, Bangladesh
  • M. Zulfikar Ali Department of Mathematics, University of Rajshai, Bangladesh
Keywords: cubic non-linearity, overdamped-oscillation, perturbation method, eigen-values


Combo overdamp-oscillatory system plays an important role in natural phenomena in many engineering problems. In this paper, fifth order nonlinear damped-oscillatory differential system is studied to investigate an asymptotic analytical approximate solution in the fashion of overdamp-oscillations via an extension of the Krylov-Bogoliubov-Mitropolskii (KBM) method. The proposed method is demonstrated by its applications on a Duffing oscillators in the combined form of overdamp and oscillatory effects. The result obtained by the presented extended technique good agreement with the numerical solutions of the fourth order Runge-Kutta method.

How to Cite
Harun-Or-Roshid and Ali, M. Z. (2020) “Asymptotic Solutions of Fifth Order Overdamped-Oscillatory Nonlinear Systems”, Contemporary Mathematics, 1(4). doi: 10.37256/cm.142020496.