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Composite Asymptotic Expansions: General Study

  • Augustin Fruchard
  • Reinhard Schäfke
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2066)

Abstract

In this chapter, we present the general theory of ca se s: their definition and their behavior with respect to the basic operations of addition, multiplication, division, differentiation, integration, composition and analytic continuation. We also link our ca se s to the inner and outer expansions of the classical method of matching. Using these inner and outer expansions is also a good method for determining the coefficients of a composite expansion in practice, provided one can show the existence of a composite expansion independently.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Augustin Fruchard
    • 1
  • Reinhard Schäfke
    • 2
  1. 1.Laboratoire de Mathématiques, Informatique et ApplicationsUniversité de Haute AlsaceMulhouseFrance
  2. 2.Institut de Recherche Mathématique AvancéeUniversité de StrasbourgStrasbourgFrance

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