Simplified error bounds for turning point expansions

被引：5
|
作者：
Dunster, T. M. [1 ]
Gil, A. [2 ]
Segura, J. [3 ]
机构：
[1] San Diego State Univ, Dept Math & Stat, 5500 Campanile Dr, San Diego, CA 92182 USA
[2] Univ Cantabria, ETSI Caminos, Dept Matemat Aplicada & CC Computac, Santander 39005, Spain
[3] Univ Cantabria, Dept Matemat Estadist & Computac, Fac Ciencias, Santander 39005, Spain
来源：
ANALYSIS AND APPLICATIONS | 2021年 / 19卷 / 04期
关键词：
Asymptotic expansions; Airy functions; turning point theory; WKB methods; ORDINARY DIFFERENTIAL-EQUATIONS; ASYMPTOTIC EXPANSIONS; BESSEL-FUNCTIONS; COMPUTATION;
D O I：
10.1142/S0219530520500104
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：647 / 678
页数：32
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