抗原 发表于 2025-3-23 12:59:24
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Uniform Transformations at Turning Points: Formal Theory, potential turning points were removed. In this chapter domains containing turning points will be considered, and the first question is: How far can the differential equation be simplified by . transformations with well understood asymptotic properties in such regions. The essence of Langer’s method叙述 发表于 2025-3-24 11:50:07
Extensions of the Regions of Validity of the Asymptotic Solutions,, neighborhoods of a point. Several techniques exist for the study of the asymptotic properties of the solutions in larger domains. Most of those methods have to be adapted to specific examples, because general theories are either too difficult or so cumbersome as to yield little insight. Here is a广口瓶 发表于 2025-3-24 15:17:39
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Doubly Asymptotic Expansions,of the asymptotic theory one has to characterize functions of x and ∈ by their behavior near x = ∞ in some unbounded region of the x-plane, the knowledge of doubly asymptotic expansions is extremely helpful. Unfortunately, all known results of some generality in this direction require that the coeffAffectation 发表于 2025-3-25 02:46:03
A Singularly Perturbed Turning Point Problem,ins positive are now commonly called “singular perturbation problems.” The condition that the order remain positive for ∈ = 0 is not a very distinguishing property of the differential equation as such. The equation . . a constant,for instance, which will be examined closely in the next section, beco