Singular perturbation refers to a situation in mathematical analysis, particularly in the study of differential equations, where a small parameter multiplies the highest derivative in the equation. This small parameter can lead to significant changes in the behavior of the solution, resulting in phenomena that cannot be understood by analyzing the equation without this parameter. In this context, singular perturbations typically give rise to boundary layers — regions where the solution changes rapidly compared to other regions.
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A singular perturbation multiplies a highest derivative or otherwise changes the limiting equation's order when its small parameter is set to zero. It commonly separates fast and slow time scales.