ASYMPTOTIC SOLUTION OF SECOND ORDER OVER-DAMPED NON-LINEAR SYSTEMS FOR SMALL RATIO OF THE EIGENVALUES

A technique is developed for obtaining the solution of second order over-damped non-linear systems based on the Krylov-Bogoliubov-Mitropolskii (KBM) method for small ratio of the eigenvalues. The solution is also useful for large ratio of the eigenvalues. The method is illustrated by an example.