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Simplified error bounds for turning point expansions

Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182, USA

Corresponding author.

Departamento de Matemática, Aplicada y CC. de la Computación, ETSI Caminos, Universidad de Cantabria, 39005 Santander, Spain

E-mail Address: amparo.gil@unican.es

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J. Segura

Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39005 Santander, Spain

E-mail Address: javier.segura@unican.es

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https://doi.org/10.1142/S0219530520500104Cited by:8 (Source: Crossref)

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.

Keywords:

AMSC: 34E05, 33C10, 34E20

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