Approximate Solution of a Fourth Order Weakly Non-Linear Differential System with Strong Damping and Slowly Varying Coefficients by Unified KBM Method

Authors

  • M Alhaz Uddin Department of Mathematics, Rajshahi University, Rajshahi
  • MA Sattar Department of Mathematics, Rajshahi University, Rajshahi

DOI:

https://doi.org/10.3329/jbas.v34i1.5493

Keywords:

Perturbation method, Weak nonlinearity, Oscillatory process, Strong damping, Varying coefficients

Abstract

The unified Krylov-Bogoliubov-Mitropolskii (KBM) method is used for determining the
analytical approximate solution of a fourth order weakly nonlinear differential system with strong
damping and slowly varying coefficients when a pair of eigen-values of the unperturbed equation
is a multiple (approximately or perfectly) of the other pair or pairs. In a damped case, one of the
natural frequencies of the linearized equation may be a multiple of the other. The analytical first
order approximate solution for different initial conditions shows a good coincidence with those
obtained by the numerical procedure. The method is illustrated by an example.

Key words: Perturbation method; Weak nonlinearity; Oscillatory process; Strong damping; Varying coefficients

DOI: 10.3329/jbas.v34i1.5493

Journal of Bangladesh Academy of Sciences, Vol.34, No.1, 71-82, 2010

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How to Cite

Uddin, M. A., & Sattar, M. (2010). Approximate Solution of a Fourth Order Weakly Non-Linear Differential System with Strong Damping and Slowly Varying Coefficients by Unified KBM Method. Journal of Bangladesh Academy of Sciences, 34(1), 71–82. https://doi.org/10.3329/jbas.v34i1.5493

Issue

Vol. 34 No. 1 (2010)

Section

Articles