Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended for solving fourth order more critically damped non-linear systems. For different damping forces, the solutions obtained by the present method show good coincidence with numerical solutions. The method is illustrated by an example.
By means of the extended Krylov-Bogoliubov-Mitropolskii method, an asymptotic solution of second order over-damped nonlinear system is found. The results obtained by this method are exactly same as the results obtained by Murty et al. (1969). The determination of the solution followed by Murty et al. (1969) is too much laborious and cumbersome. On the contrary, the present method is very simple and easier. It is illustrated by an example.
A second order nonlinear differential system modeling non-oscillatory processes by over damping is considered. Then second order approximate solution is found by means of an extension of the Krylov-Bogoliubov-Mitropolskii (KBM) method. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical solution.
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