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Popov, I. P., “A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russian),” Dokl. Akad. USSR, 3. 308-310. 1956.

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Article

Asymptotic Solutions of Fifth Order More Critically Damped Nonlinear Systems in the Case of Four Repeated Roots

1Department of Mathematics, Islamic University, Kushtia, Bangladesh

2Department of Computer Science & Engineering, Z.H. Sikder University of Science & Technology, Shariatpur, Bangladesh


American Journal of Applied Mathematics and Statistics. 2015, Vol. 3 No. 6, 233-242
DOI: 10.12691/ajams-3-6-4
Copyright © 2015 Science and Education Publishing

Cite this paper:
M. Abul Kawser, Md. Mahafujur Rahaman, Md. Shajib Ali, Md. Nurul Islam. Asymptotic Solutions of Fifth Order More Critically Damped Nonlinear Systems in the Case of Four Repeated Roots. American Journal of Applied Mathematics and Statistics. 2015; 3(6):233-242. doi: 10.12691/ajams-3-6-4.

Correspondence to: Md.  Mahafujur Rahaman, Department of Computer Science & Engineering, Z.H. Sikder University of Science & Technology, Shariatpur, Bangladesh. Email: mahfuz0809@gmail.com

Abstract

In this article, we have modified the Krylov-Bogoliubov-Mitropolskii (KBM) method, which is one of the most widely used methods to delve into the transient behavior of oscillating systems, to find out the solutions of fifth order more critically damped nonlinear systems. In this paper, we have considered the asymptotic solutions of fifth order more critically damped nonlinear systems when the four eigenvalues are equal and another one is distinct. This article suggests that the perturbation solutions obtained by the modified KBM method for both the cases (when repeated eigenvalues are greater than the distinct eigenvalue, and when the distinct eigenvalue is greater than repeated eigenvalues) satisfactorily correspond to the numerical solutions obtained by Mathematica 9.0.

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