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20. 9. 2018.
Closeness of Solutions for Singularly Perturbed Systems via Averaging
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order $\mathcal{O} (\sqrt{\varepsilon})$, where $\varepsilon$ is the perturbation parameter.