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Analytical Approximate Solutions of Fifth Order More Critically Damped Nonlinear Systems

Md. Mahafujur Rahaman, M. Abul Kawser


This studymodifies the Krylov-Bogoliubov-Mitropolskii (KBM) method, 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, and considers asymptotic solutions when the triply eigenvalues are large and the other two equal eigenvalues are small. The study reveals that the solutions obtained by the modified KBM method satisfactorilycorrespond to those obtained by the fourth order Runge-Kuttamethod.


KBM method, more critically damped system,nonlinearity, eigenvalues.

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