HIGHER ORDER IMPROVED SOLUTION OF SECOND ORDER OVER-DAMPED NON-LINEAR SYSTEMS
DOI:
https://doi.org/10.53808/KUS.2007.8.1.0635-PSKeywords:
Perturbation, asymptotic solutions, over-damping, non-linear systemAbstract
A second order nonlinear differential system modeling non-oscillatory processes by over damping is considered. Then second order approximate solution is found by means of an extension of the Krylov-Bogoliubov-Mitropolskii (KBM) method. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical solution.
Downloads
References
Alam, S. 2002. A unified Krylov-Bogoliubov-Mitropolskii method for Solving n - th order nonlinear systems. Journal of Franklin Institute, 339: 239-248.
Bogoliubov, N.N. and Mitropolskii, Yu. 1961. Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordan and Breach, New York.
Bojadziev, G.N. 1983. Damped Nonlinear Oscillations Modeled by a 3-dimensional Differential System. Acta Mechanica, 48: 193-201.
Krylov, N.N. and Bogoliubov, N.N. 1947. Introduction to nonlinear mechanics. Princeton University presses, New Jersey.
Mendelson, K.S. 1970. Perturbation theory for damped nonlinear oscillations. Journal of Mathematical Physics, 2: 3413-3415.
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.
Popov, I.P. 1956. A generalization of the Bogoliubov asymptotic methods in the theory of nonlinear oscillations. Dokl. Nauk. USSR. 3: 308-310 (in Russian).
Sattar, M.A. 1986. An Asymptotic Method for second order critically damped nonlinear equations. Journal of Franklin Institute, 321: 109-113.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Khulna University Studies
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.