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This paper studies the behavior of singularly perturbed nonlineardifferential equations with boundary-layer solutions that do not necessarilyconverge to an equilibrium. Using the average of the fast variable and assumingthe boundary layer solutions converge to a bounded set, results on thecloseness of solutions of the singularly perturbed system to the solutions ofthe reduced average and boundary layer systems over a finite time interval arepresented. The closeness of solutions error is shown to be of orderO(\sqrt(\epsilon)), where \epsilon is the perturbation parameter.

Closeness of Solutions for Singularly Perturbed Systems via Averaging