Extrapolation of perturbation-theory expansions by self-similar approximants

The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their us...

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Bibliographic Details
Published in:European journal of applied mathematics Vol. 25; no. 5; pp. 595 - 628
Main Authors: GLUZMAN, S., YUKALOV, V.I.
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.10.2014
Subjects:
Applied mathematics
Approximants
Approximation
Asymptotic expansions
Asymptotic methods
Asymptotic properties
Extrapolation
Mathematical analysis
Self-similarity
Function-theoretic methods
Approximation with constraints
Functional analytic methods of summability
Approximation to limiting values
Approximation by arbitrary nonlinear expressions
ISSN:0956-7925, 1469-4425
Online Access:Get full text
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Summary:The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures.
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ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792514000163