2019/09/30 by T. M. Dunster, Amparo Gil, Dunster, T. M. +3 · 1 citation
Computer Science · Mathematics · #34E05 (Primary) 33C10 #34E20 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1909.13415
openalex publication_date 2019/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 F. W. J. Olver.