Singular Perturbation

A singular perturbation problem depends on a small parameter in such a way that setting changes the order, type, or number of conditions of the problem. For example, the coefficient of the highest derivative in a differential equation may vanish with . An ordinary power series expansion then generally fails to be uniform, and the solution can contain boundary layers or rapidly varying regions. Techniques for singular perturbations include matched asymptotic expansions and the method of multiple scales.