Asymptotic Method of Krylov-Bogoliubov-Mitropolskii for Fifth Order Critically Damped Nonlinear Systems
Applied and Computational Mathematics
Volume 4, Issue 6, December 2015, Pages: 387-395
Received: Aug. 26, 2015; Accepted: Sep. 19, 2015; Published: Sep. 29, 2015
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Authors
Md. Nazrul Islam, Department of Mathematics, Islamic University, Kushtia, Bangladesh
Md. Mahafujur Rahaman, Department of Computer Science & Engineering, Z. H. Sikder University of Science & Technology, Shariatpur, Bangladesh
M. Abul Kawser, Department of Mathematics, Islamic University, Kushtia, Bangladesh
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Abstract
In oscillatory problems, the method of Krylov–Bogoliubov–Mitropolskii (KBM) is one of the most used techniques to obtain analytical approximate solution of nonlinear systems with a small non-linearity. This article modifies the KBM method to examine the solutions of fifth order critically damped nonlinear systems with four pairwise equal eigenvalues and one distinct eigenvalue, in which the latter eigenvalue is much larger than the former four pairwise eigenvalues. This paper suggests that the results obtained in this study correspond accurately to the numerical solutions obtained by the fourth order Runge-Kutta method. This paper, therefore, concludes that the modified KBM method provides highly accurate results, which can be applied for different kinds of nonlinear differential systems.
Keywords
KBM, Asymptotic Method, Critically Damped System, Nonlinearity, Runge-Kutta Method, Eigenvalues
To cite this article
Md. Nazrul Islam, Md. Mahafujur Rahaman, M. Abul Kawser, Asymptotic Method of Krylov-Bogoliubov-Mitropolskii for Fifth Order Critically Damped Nonlinear Systems, Applied and Computational Mathematics. Vol. 4, No. 6, 2015, pp. 387-395. doi: 10.11648/j.acm.20150406.11
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