Krylov-Bogoliubov-Mitropolskii method is modified and applied to certain damped nonlinear systems with slowly varying coefficients. The results obtained by this method show excellent coincidence with those obtained by numerical method. The method is illustrated by an example.
| DOI | 10.11648/j.pamj.20130201.14 |
| Published in | Pure and Applied Mathematics Journal (Volume 2, Issue 1, February 2013) |
| Page(s) | 28-31 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Perturbation Methods, Varying Coefficient, Unperturbed Equation, Nonlinear Differential Systems, Damped System
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| [2] | N. N, Bogoliubov and Yu. Mitropolskii, Asymptotic Methods in the Theory of nonlinear Oscillations, Gordan and Breach, New York, 1961. |
| [3] | Yu.,Mitropolskii, "Problems on Asymptotic Methods of Non-stationary Oscillations" (in Russian), Izdat, Nauka, Moscow, 1964. |
| [4] | I. P. Popov, "A generalization of the Bogoliubov asymptotic method in the theory of nonlinear oscillations", Dokl.Akad. Nauk SSSR 111, 1956, 308-310 (in Russian). |
| [5] | I. S. N. Murty, B. L. Deekshatulu and G. Krisna, "General asymptotic method of Krylov-Bogoliubov for over-damped nonlinear system", J. Frank Inst. 288 (1969), 49-46. |
| [6] | I.S.N. Murty, "A Unified Krylov-Bogoliubov Method for Second Order Nonlinear Systems", Int. J. nonlinear Mech., 6, 1971, pp45-53. |
| [7] | M.,Shamsul Alam, "Unified Krylov- Bogoliubov- Mitro-polskii Method for Solving n-th Order Nonlinear System with Slowly Varying Coefficients", Journal of Sound and Vibration, 256, 2003, pp987-1002. |
| [8] | Cheng Hung and Tai Tsun Wu, An Aging Spring, Studies in Applied Mathematics, 49, 1970. pp183-185. |
| [9] | K.C. Roy and M. Shamsul Alam, Effects of Higher Ap-proximation of Krylov- Bogoliubov-Mitropolskii Solution and Matched Asymptotic Solution of a Differential System with Slowly Varying Coefficients and Damping Near to a Turning Point, Vietnam Journal of Mechanics, VAST, 26, 2004.,pp182-192. |
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| [11] | Pinakee Dey., Harun or Rashid, M. Abul Kalam Azad and M S Uddin, "Approximate Solution of Second Order Time Dependent Nonlinear Vibrating Systems with Slowly Varying Coefficients", Bull. Cal. Math. Soc, 103, (5), 2011. pp 371-38. |
| [12] | Pinakee Dey, Md. Babul Hossain, Md. Musa Miah and Mo-hammad Mokaddes Ali,." Approximate solutions of damped nonlinear vibrating system with varying coefficients under some conditions" Applied and Computational Mathematics. 1(2), 2012, pp 1-6. |
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APA Style
Pinakee Dey. (2013). Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces. Pure and Applied Mathematics Journal, 2(1), 28-31. https://doi.org/10.11648/j.pamj.20130201.14
ACS Style
Pinakee Dey. Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces. Pure Appl. Math. J. 2013, 2(1), 28-31. doi: 10.11648/j.pamj.20130201.14
AMA Style
Pinakee Dey. Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces. Pure Appl Math J. 2013;2(1):28-31. doi: 10.11648/j.pamj.20130201.14
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Download@article{10.11648/j.pamj.20130201.14,
author = {Pinakee Dey},
title = {Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces},
journal = {Pure and Applied Mathematics Journal},
volume = {2},
number = {1},
pages = {28-31},
doi = {10.11648/j.pamj.20130201.14},
url = {https://doi.org/10.11648/j.pamj.20130201.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130201.14},
abstract = {Krylov-Bogoliubov-Mitropolskii method is modified and applied to certain damped nonlinear systems with slowly varying coefficients. The results obtained by this method show excellent coincidence with those obtained by numerical method. The method is illustrated by an example.},
year = {2013}
}
TY - JOUR T1 - Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces AU - Pinakee Dey Y1 - 2013/02/20 PY - 2013 N1 - https://doi.org/10.11648/j.pamj.20130201.14 DO - 10.11648/j.pamj.20130201.14 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 28 EP - 31 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20130201.14 AB - Krylov-Bogoliubov-Mitropolskii method is modified and applied to certain damped nonlinear systems with slowly varying coefficients. The results obtained by this method show excellent coincidence with those obtained by numerical method. The method is illustrated by an example. VL - 2 IS - 1 ER -
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