Simplified error bounds for turning point expansions

Dunster, T. M.; Gil Gómez, Amparo; Segura Sala, José Javier

doi:10.1142/S0219530520500104

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SimplifieldErrorBoun ... (16.76Mb)

Identificadores

URI: http://hdl.handle.net/10902/21839

DOI: 10.1142/S0219530520500104

ISSN: 0219-5305

ISSN: 1793-6861

Fecha

2021-07

Derechos

Electronic version of an article published as Analysis and ApplicationsVol. 19, No. 04, pp. 647-678 (2021) https://doi.org/10.1142/S0219530520500104 © World Scientific Publishing Company https://www.worldscientific.com/worldscinet/aa"

Publicado en

Analysis and Applications, Vol. 19, No. 04, pp.647-678

Editorial

World Scientific

Enlace a la publicación

https://doi.org/10.1142/S0219530520500104

Palabras clave

Asymptotic expansions

Airy functions

Turning point theory

WKB methods

Resumen/Abstract

ABSTRACT: Recently, the present authors derived new asymptotic expansions for linear differential equations having a simple turning point. These involve Airy functions and slowly varying coefficient functions, and were simpler than previous approximations, in particular being computable to a high degree of accuracy. Here we present explicit error bounds for these expansions which only involve elementary functions, and thereby provide a simplification of the bounds associated with the classical expansions of Olver.