We present preliminary results on a new perturbation technique that combines the fundamental elements of the methods of equivalent linearization and first-order averaging. The importance of this procedure is derived from the fact that it can be applied to ODE’s having oscillatory solutions, but for which no harmonic oscillator limiting equation exists. The procedure is illustrated by showing how it can be used to calculate analytical approximations to two nonlinear ODE’s. Comparison with the corresponding accurate numerical solutions is also given. The work presented here was supported in part by research grants from DOE and the MBRS-SCORE Program at Clark Atlanta University.

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