ANALYSIS AND IMPROVEMENT OF DIVERGENT SERIES

A recent paper by Van Dyke (1) discusses how convergent perturbation series may be analysed and improved when only the first few terms are known. In this paper two methods are described for improving the usefulness of divergent series. The examples chosen to illustrate the methods are the classical...

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Bibliographic Details
Published in:Quarterly journal of mechanics and applied mathematics 1976-05, Vol.29 (2), p.127-135
Main Author: BUCHANAN, D. J.
Format: Article
Language:English
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Summary:A recent paper by Van Dyke (1) discusses how convergent perturbation series may be analysed and improved when only the first few terms are known. In this paper two methods are described for improving the usefulness of divergent series. The examples chosen to illustrate the methods are the classical second virial coefficient for the Lennard–Jones (6–12) potential and the Rayleigh–Schrödinger expansion for the ground-state energy of the anharmonic oscillator.
ISSN:0033-5614
1464-3855
DOI:10.1093/qjmam/29.2.127