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Asymptotic analysis, Working Note No. 1 [electronic resource] : Basic concepts and definitions

Published
Washington, D.C. : United States. Dept. of Energy, 1993.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
Physical Description
16 pages : digital, PDF file
Additional Creators
Argonne National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
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Summary
In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest we begin by defining the order relations O, o, and O{sup {number_sign}}, which enable us to compare the asymptotic behavior of functions of a small positive parameter ε as ε ↓ 0. Next, we introduce order functions, asymptotic sequences of order functions and more general gauge sets of order functions and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set. This string of definitions culminates in the introduction of the concept of a regular asymptotic expansion, also known as a Poincare expansion, of a function f : (0, ε{sub o}) → X, where X is a normed vector space of functions defined on a domain D ε R{sup N}. We conclude the note with the asymptotic analysis of an initial value problem whose solution is obtained in the form of a regular asymptotic expansion.
Report Numbers
E 1.99:anl/mcs-tm--179
anl/mcs-tm--179
Subject(s)
Other Subject(s)
Note
Published through SciTech Connect.
07/01/1993.
"anl/mcs-tm--179"
"DE94001000"
Kaper, H.G.; Garbey, M.
Type of Report and Period Covered Note
Topical; 07/01/1993 - 07/01/1993
Funding Information
W-31109-ENG-38
View MARC record | catkey: 14353104