On some special conditions of $n$-th order non-oscillatory nonlinear systems
Commun. Korean Math. Soc. 2003 Vol. 18, No. 4, 755-765 Printed December 1, 2003
M. Shamsul Alam, M. B. Hossain Bangladesh Institute of Technology, Bangladesh Institute of Technology
Abstract : Krylov-Bogoliubov-Mitropolskii method has been extended to obtain asymptotic solution of $n$-th order nonlinear differential system characterized by certain non-oscillatory processes. The damping force is considered in such a manner that one of the characteristic roots of the linear system becomes small and others are in integral multiple. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical method.
Keywords : asymptotic expansion, non-oscillation, over-damped systems