Uniform asymptotics as a stationary point approaches an endpoint

Arran Fernandez, Euan Spence, A S Fokas

Research output: Contribution to journalArticle

Abstract

We obtain the rigorous uniform asymptotics of a particular integral where a stationary point is close to an endpoint. There exists a general method introduced by Bleistein for obtaining uniform asymptotics in this situation. However, this method does not provide rigorous estimates for the error. Indeed, the method of Bleistein starts with a change of variables, which implies that the parameter governing how close the stationary point is to the endpoint appears in several parts of the integrand, and this means that one cannot obtain general error bounds. By adapting the above method to our particular integral, we obtain rigorous uniform leading-order asymptotics. We also give a rigorous derivation of the asymptotics to all orders of the same integral; the novelty of this second approach is that it does not involve a global change of variables.
Original languageEnglish
Pages (from-to)204-242
Number of pages39
JournalIMA Journal of Applied Mathematics
Volume83
Issue number1
Early online date4 Jan 2018
DOIs
Publication statusPublished - 1 Feb 2018

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Uniform Asymptotics
Stationary point
Change of Variables
Integrand
Error Bounds
Imply
Estimate

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Uniform asymptotics as a stationary point approaches an endpoint. / Fernandez, Arran; Spence, Euan; Fokas, A S.

In: IMA Journal of Applied Mathematics, Vol. 83, No. 1, 01.02.2018, p. 204-242.

Research output: Contribution to journalArticle

Fernandez, Arran ; Spence, Euan ; Fokas, A S. / Uniform asymptotics as a stationary point approaches an endpoint. In: IMA Journal of Applied Mathematics. 2018 ; Vol. 83, No. 1. pp. 204-242.
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