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The Use of an lnvariance Condition in the Solution of Multiple‐Scale Singular Perturbation Problems: Ordinary Differential Equations
Author(s) -
Woodruff S. L.
Publication year - 1993
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/sapm1993903225
Subject(s) - singular perturbation , mathematics , a priori and a posteriori , ordinary differential equation , perturbation (astronomy) , mathematical analysis , poincaré–lindstedt method , scale (ratio) , method of matched asymptotic expansions , differential equation , physics , philosophy , epistemology , quantum mechanics
A new method is proposed for the solution of multiple‐scale perturbation problems. The straightforward perturbation solution, with secular terms, is used to construct a uniformly‐valid solution by enforcing an invariance property implicit in the expansion procedure. It is suggested that this method is more systematic than many methods currently in use and requires fewer a priori assumptions about the nature of the solution. A proof of the asymptotic validity of the method is given and some examples are presented.