ON FOURTH ORDER MORE CRITICALLY DAMPED NON-LINEAR SYSTEMS UNDER SOME CONDITIONS

Mo. Rokibul  Islam; M. Ali  Akbar; B.M. Ikramul  Haque; M.  Samsuzzoha; Zasmin  Haque; Afroza Ali  Soma

doi:10.53808/KUS.2007.8.1.0643-PS

Authors

Mo. Rokibul Islam Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
M. Ali Akbar Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
B.M. Ikramul Haque Department of Mathematics, Khulna University of Engineering and Technology, Khulna 9203, Bangladesh
M. Samsuzzoha Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
Zasmin Haque Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
Afroza Ali Soma Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh

DOI:

https://doi.org/10.53808/KUS.2007.8.1.0643-PS

Keywords:

Perturbation, asymptotic solutions, more critically damping

Abstract

Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended for solving fourth order more critically damped non-linear systems. For different damping forces, the solutions obtained by the present method show good coincidence with numerical solutions. The method is illustrated by an example.

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References

Akbar, M.A.; Alam, S. and Sattar, M.A. 2003. Asymptotic method for fourth order damped nonlinear systems. Ganit, Journal of Bangladesh Mathematical Society, 23: 72-80.

Akbar, M.A.; Alam, S. and Sattar, M.A. 2005. A simple technique for obtaining certain over-damped solutions of an n-th order nonlinear differential equation. Soochow Journal of Mathematics, 31(2): 291-299.

Alam, S. and Sattar, M.A. 1996. An asymptotic method for third order critically damped nonlinear equations. Journal of Mathematical and Physical Sciences, 30: 291-298.

Alam, S. and Sattar, M.A. 1997. A unified Krylov-Bogoliubov-Mitropolskii method for solving third order nonlinear systems. Indian Journal of Pure and Applied Mathematics, 28: 151-167.

Alam, S. 2001. Asymptotic methods for second order over-damped and critically damped nonlinear systems. Soochow Journal of Mathematics, 27: 187-200.

Alam, S. 2002a. Bogoliubov's method for third order critically damped nonlinear systems. Soochow Journal of Mathematics, 28: 65-80.

Alam, S. 2002b. On some special conditions of third order over-damped nonlinear systems. Indian Journal of Pure and Applied Mathematics, 33: 727-742.

Alam, S. 2002c. A unified Krylov-Bogoliubov-Mitropolskii method for solving n-th order nonlinear systems. Journal of Franklin Institute, 339: 239-248.

Alam, S. 2002d. Asymptotic method for non-oscillatory nonlinear systems. Far East Journal of Applied Mathematics, 7: 119-128.

Alam, S. 2002e. On some special conditions of over-damped nonlinear systems. Soochow Journal of Mathematics, 29: 181-190.

Bogoliubov, N.N. and Mitropolskii, Yu. 1961. Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordan and Breach, New York.

Islam, M.R.; Akbar, M.A.; Samsuzzoha, M. and Soma, A.A. 2006. New technique for third order critically damped non-linear systems. Acta Mathematica Vietnamica, (Submitted).

Islam, M.R.; Akbar, M.A.; Haque, Z. and Soma, A.A. 2006. New technique for fourth order critically damped non-linear systems. Indian Journal of Theoretical Physics, (Submitted).

Krylov, N.N. and Bogoliubov, N.N. 1947. Introduction to Nonlinear Mechanics. Princeton University Presses, New Jersey.

Murty, I.S.N. 1971. A unified Krylov-Bogoliubov method for solving second order nonlinear systems. Instituted Journal of Nonlinear Mechanics, 6: 45-53.

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.

Sattar, M.A. 1986. An asymptotic method for second order critically damped nonlinear equations. Journal of Franklin Institute, 321: 109-113.

Sattar, M.A. 1993. An asymptotic method for three-dimensional over-damped nonlinear systems. Ganit, Journal of Bangladesh Mathematical Society, 13: 1-8.