PERTURBATION SOLUTIONS OF FIFTH ORDER MORE CRITICALLY DAMPED NONLINEAR SYSTEMS WITH LARGE EQUAL EIGENVALUES

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Published: 2017-09-25

Page: 109-124


MD. MAHAFUJUR RAHAMAN *

Department of Computer Science and Engineering, Z. H. Sikder University of Science and Technology, Shariatpur-8024, Bangladesh

M. ABUL KAWSER

Department of Mathematics, Islamic University, Kushtia-7003, Bangladesh

*Author to whom correspondence should be addressed.


Abstract

In this article, the Krylov-Bogoliubov-Mitropolskii (KBM) method, which is considered to be one of the most convenient and widely used methods of studying the transient behavior of nonlinear systems, is extended with a view to finding out the solutions of fifth order more critically damped nonlinear systems. The analytical approximate solutions of fifth more critically damped nonlinear systems are used, where the three larger eigenvalues are identical and the two others are different. In this study, it is recommended that the perturbation solutions obtained by the modified KBM method demonstrate good coincidence with the numerical solutions.

Keywords: KBM method, perturbation solution, more critically damped, nonlinearity, eigenvalues


How to Cite

RAHAMAN, M. M., & KAWSER, M. A. (2017). PERTURBATION SOLUTIONS OF FIFTH ORDER MORE CRITICALLY DAMPED NONLINEAR SYSTEMS WITH LARGE EQUAL EIGENVALUES. Asian Journal of Mathematics and Computer Research, 20(3), 109–124. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1050

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