Premium
Uniform asymptotic solutions of the orr–sommerfeld equation
Author(s) -
Baldwin P.
Publication year - 1981
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015436
Subject(s) - mathematics , neighbourhood (mathematics) , ordinary differential equation , approximations of π , mathematical analysis , differential equation , order (exchange) , finance , economics
Summary Reid (1974) derived “first approximations” to solutions of the Orr–Sommerfeld equation, which are uniformly valid in a full neighbourhood of a critical point. This paper shows that such approximations may be calculated to higher order, and makes a first step towards placing the theory on a rigorous basis by providing error bounds for the dominant‐recessive approximations. These are obtained by generalizing methods discussed by Olver (1974) for second order linear ordinary differential equations.