Abstract
The series generated by a perturbation approach does not necessarily converge. Asymptotic methods use a mathematical apparatus of a somewhat peculiar nature — asymptotic series. They diverge but still approximate the functions in hand in a certain sense. Briefly, we can say that a convergent series represents a function at x = x 0, n → ∞ (Fig. 1.1), while an asymptotic series is valid for n = n 0, x → x 0 (Fig. 1.2).
There is always a certain charm in tracing the evolution of theories in the original papers; often such study offers deeper insights into the subject matter than the systematic presentation of the final result, polished by the words of many contemporaries.
A. Einstein [632,p.244]
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© 2004 Springer-Verlag Berlin Heidelberg
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Andrianov, I., Awrejcewicz, J., Manevitch, L.I. (2004). Asymptotic Approximations. In: Asymptotical Mechanics of Thin-Walled Structures. Foundations of Engineering Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45246-1_1
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DOI: https://doi.org/10.1007/978-3-540-45246-1_1
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