Simplified error bounds for turning point expansions-Reference-Cited by-同舟云学术

Simplified error bounds for turning point expansions

Published:2020-07-03 Issue:04 Volume:19 Page:647-678
ISSN:0219-5305
Container-title:Analysis and Applications
language:en
Short-container-title:Anal. Appl.

Author:

Dunster T. M.¹,Gil A.²,Segura J.³

Affiliation:

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

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

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

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.

Funder

Ministerio de Ciencia e Innovacion Spain

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219530520500104

Reference17 articles.

1. Algorithm 644

2. Bessel Functions of Purely Imaginary Order, with an Application to Second-Order Linear Differential Equations Having a Large Parameter

3. Convergent Expansions for Solutions of Linear Ordinary Differential Equations Having a Simple Turning Point, with an Application to Bessel Functions

4. Olver's error bound methods applied to linear ordinary differential equations having a simple turning point

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