Abstract
The principal shortcoming of perturbation methods is the local nature of solutions based on them. Besides that, the following questions are very difficult for the theory: what values mayε be considered as small (large)? How can a solution for may ε be constructed if its behaviour is known for ε → 0 and ε → ∞? As the technique of asymptotic integration is well developed and widely used, such problems as elimination of the locality of expansion, evaluation of the convergence domain, construction of uniformly suitable solutions are very urgent.
One can calculate only a few terms of perturbation expansion, usually no more then two or three, and almost never more than seven. The resulting series is often slowly convergent, or even divergent. Yet those few terms contain a remarkable amount of information, which the investigator should do his best to extract [660,p.202].
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© 2004 Springer-Verlag Berlin Heidelberg
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Andrianov, I., Awrejcewicz, J., Manevitch, L.I. (2004). Improvement of Perturbation Series. In: Asymptotical Mechanics of Thin-Walled Structures. Foundations of Engineering Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45246-1_13
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DOI: https://doi.org/10.1007/978-3-540-45246-1_13
Publisher Name: Springer, Berlin, Heidelberg
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