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Asymptotic solutions of inhomogeneous differential equations having a turning point
Author(s) -
Dunster T. M.
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12326
Subject(s) - airy function , method of matched asymptotic expansions , simple (philosophy) , mathematics , polynomial , exponential function , mathematical analysis , asymptotic analysis , differential equation , forcing (mathematics) , turning point , argument (complex analysis) , point (geometry) , physics , geometry , philosophy , biochemistry , chemistry , epistemology , acoustics , period (music)
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The asymptotic approximations are uniformly valid for unbounded complex values of the argument, and are applied to inhomogeneous Airy equations having polynomial and exponential forcing terms. Error bounds are available for all approximations, including new simple ones for the well‐known asymptotic expansions of Scorer functions of large complex argument.