Authors:
M. Ali Akber,Md. Sharif Uddin,Mo. Rokibul Islam,Afroza Ali Soma,DOI NO:
https://doi.org/10.26782/jmcms.2007.07.00008Keywords:
critically damped,non-linear system,KBM method,Runge-Kutta method,Abstract
Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended for sotaining of forth order more Critically Damped Nonlinear Systems. The results obtained by the presented KBM method show good coincidence with numerical results obtained by Runge-Kutta method. The method is illustrated by an example.Refference:
I. Ali Akber, M., M.A. Sattar and A.C. Paul, An Asymptotic Method of Krylov-Bogoliubov for Forth Order-Damped Nonliner Systems, Ganit. J. Bangladesh Math. Soc., vol.22, pp.83-96, 2002.
II. Ali Akber, M., M.Shyamsul Alam and M.A.Satter, Asymptotic Method for Forth Order-Damped Nonliner Systems, Ganit. J. Bangladesh Math. Soc., vol.23, pp.41-49, 2003.
III. Ali Akber, M., M.Shyamsul Alam and M.A.Satter, A Simple Technique for Obtaining Certain Over-damped Solutions of n-th order Nonlinear Differential equation, Soochow Journal of Mathematics vol.31(2), pp.291-299, 2005.
IV. Bogoliubov, N.N. and Yu. Mitropolskii, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordan and Breach, New York. 1961.
V. Krylov, N.N and N.N. Bogoliubov, Introduction to Nonlinear Mechanics, Princeton University Press, New Jersey, 1947.
VI. Mendelson, K.S., Perturbation Theory for Damped Nonlinear Oscillations, J. Math. Physics, Vol.2, pp.3413-3415,1970.
VII. Murty, I.S.N., B.L.Deekshatulu and G. Krishna, on an Asymptotic Method of krylov-Bogoliubov for Over-damped Nonlinear Systems, J. Frank. Inst. Vol.288, pp.49-65. 1969.
VIII. Murty, I.S.N., A Unified Krylov-Bogoliubov method for Solving Order Nonlinear Systems, Int. J. Nonlinear Mech. Vol.6, pp.45-53, 1971.
IX. Popov, I.P., A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russia), Doll. Akad. USSR vol.3, pp.308-310, 1956.
X. Rokibul Islam M., M.Ali Akber, M.Samsuzzoha and Afroza Ali Soma, New Technique for Third order Critically Damped Nonlinear Systems, Acta Mathematics Vietnamica.
XI. Rokibul Islam M., Md. Sharif Uddin, M. Ali Akber, M. Azmol Huda and S.M.S Hossain, New Technique for Fourth Order Critically Damped Nonlinear Systems, Calcutta Math. Soc.
XII. Sattar, M.A., An Asymptotic Method for second order Critically Damped Nonlinear Equations, J.Frank. Inst. Vol.321, pp.109-113,1986.
XIII. Sattar, M.A., An Asymptotic Method for Three-dimensional Over-damped Nonlinear Systems, Ganit, J. Bangladesh Math. Soc., Vol.13, pp.1-8, 1993.
XIV. Shamsul Alam, M. and M.A. Satter, an Asymptotic Method for third order Critically Damped Nonlinear Equations, J. Mathematical and physical Sciences, vol.30, pp.291-298,1996.
XV. Shamsul Alam M. Asymptotic Methods for Second order Over-damped and Critically Damped Nonlinear Systems, Soochow Journal of Math. Vol.27, pp.187-200, 2001.
XVI. Shamsul Alam M., Bogoliubov’s method for third Order Critically Damped Nonlinear Systems, Soochow J. Math. vol.28, pp.65-80,2002.
XVII. Shamsul Alam M., On some Special Conditions of Third order Over-damped Nonlinear Systems, Indian J. Pure appl. Math. vol.33, pp.727-742, 2002.
XVIII. Shamsul Alam M., A Unified Krylov-Bogoliubov-Mitropolskii Method for Solving n-th order Nonlinear Systems, J. Frank. Inst. vol.339, pp.239-248, 2002.
XIX. Shamsul Alam M., Asymptotic Method for non-oscillatory Nonlinear Systems, Far East J. Appl. Math., vol.7, pp.119-128, 2002.
M. Ali Akbar, Md Sharif Uddin, Md. Rokibul Islam,Afroza Ali Soma View Download