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

M. Abul Kawser¹, Md. Mahafujur Rahaman^2, , Md. Shajib Ali¹ and Md. Nurul Islam¹

¹Department of Mathematics, Islamic University, Kushtia, Bangladesh

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

Cite this paper

M. Abul Kawser, Md. Mahafujur Rahaman, Md. Shajib Ali and 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

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.

Keywords

KBM, asymptotic solution, more critically damped system, nonlinearity, eigenvalues

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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