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Uniform Asymptotic Approximations to the Solutions of the Orr‐Sommerfeld Equation Part 2. The General Theory
Author(s) -
Reid W. H.
Publication year - 1974
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 - 10.1002/sapm1974533217
Subject(s) - simple (philosophy) , mathematics , heuristic , approximations of π , asymptotic analysis , asymptotic expansion , point (geometry) , mathematical analysis , order (exchange) , method of matched asymptotic expansions , differential equation , mathematical optimization , geometry , philosophy , epistemology , finance , economics
This paper deals with the derivation of “first approximations” to the solutions of the Orr‐Sommerfeld equation which are uniformly valid in a full neighborhood of the critical point. To this order the theory is remarkably simple. The essential elements in the theory are all well known from the older heuristic theories but its general structure is substantially different. The uniform approximations are also vastly simpler than the composite approximations obtained recently by the method of matched asymptotic expansions.