A hybrid multiple scale procedure for boundary layers involving several dissimilar scales
Many boundary value problems involving rapidly decaying oscillations can be put into the form \(\varepsilon \frac {d^{2}f}{dx^2}+a(x)\frac{df}{dx}+b(x)f=0\), \(x \in{[0,1]}\), where \(0<\varepsilon \ll 1\), \(a(x)\) and \(b(x)\) are continuous functions of \(x\), and \(f\) varies rapidly in regions of \(x\). The aim of this article is to devise a method to solve such problems by using well-known perturbation methods which involve four widely varying scales for independent variables. The author suggests such a composite scale which can be reduced to the dissimilar scales in the corresponding intervals and leads to an accurate uniformly valid solution.
scientific article; zbMATH DE number 1251166