  This is a regular limit—there are no singularities or “blowups” as the asymptotic limit is approached. As noted one way of thinking about this is that the exact solutions for small but nonzero values of \(|\varepsilon\)| “smoothly [approach] the unperturbed or zeroth-order solution [\(\varepsilon\) set identically equal to zero] as \(\varepsilon \rightarrow 0\).” In the case where the limit is singular “the exact solution for \(\varepsilon = 0\) is fundamentally different in character from the ‘neighboring’ solutions obtained in the limit \(\varepsilon \rightarrow 0\).” (Bender and Orszag 1978, 324)