ASYMPTOTIC SOLUTION OF SECOND ORDER OVER-DAMPED NON-LINEAR SYSTEMS FOR SMALL RATIO OF THE EIGENVALUES

Authors

  • Mo. Rokibul Islam Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh
  • M. Mizanur Rahman Department of Mathematics, Islamic University, Kushtia-7003, Bangladesh
  • M. Ali Akbar Department of Applied Mathematics, Rajshahi University, Rajshahi-6205, Bangladesh
  • M. Sharif Uddin Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh

DOI:

https://doi.org/10.53808/KUS.2008.9.2.0840-PS

Keywords:

Perturbation, Asymptotic Solution, Over-Damped

Abstract

A technique is developed for obtaining the solution of second order over-damped non-linear systems based on the Krylov-Bogoliubov-Mitropolskii (KBM) method for small ratio of the eigenvalues. The solution is also useful for large ratio of the eigenvalues. The method is illustrated by an example.

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References

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Islam, M. R.; Akbar, M. A.; Haque, B. M. I.; Haque, Z. and Soma, A. A. 2007. On Fourth Order More Critically Damped Non-linear Systems Under Some Conditions, Khulna University Studies, 8(1): 125-134.

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Murty, I. S. N.; Deekshatulu B. L. and Krishna, G. 1969. On an Asymptotic Method of Krylov-Bogoliubov for Over-damped Nonlinear Systems, Journal of Franklin Institute, 288: 49-65.

Murty, I. S. N. 1971. A Unified Krylov-Bogoliubov Method for Solving Second Order Nonlinear Systems, International Journal of Nonlinear Mechanics, 6: 45-53.

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

Sattar, M. A. 1986. An asymptotic Method for Second Order Critically Damped Nonlinear Equations, Journal of Franklin Institute, 321: 109-113.

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Published

23-11-2008

How to Cite

[1]
M. R. Islam, M. M. . Rahman, M. A. Akbar, and M. S. . Uddin, “ASYMPTOTIC SOLUTION OF SECOND ORDER OVER-DAMPED NON-LINEAR SYSTEMS FOR SMALL RATIO OF THE EIGENVALUES”, Khulna Univ. Stud., pp. 341–346, Nov. 2008.

Issue

Section

Physical Science

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