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The Comparison Method

  • N. Rouche
  • P. Habets
  • M. Laloy
Part of the Applied Mathematical Sciences book series (AMS, volume 22)

Abstract

The role of the comparison method, as already studied in Section II.3, might be roughly characterized as follows: the solutions of the comparison equation push on before themselves those of the original equation. Following V. M. Matrosov [1973], this can be viewed as an interesting extension of the notion of a mathematical model. In the usual sense, a mathematical model operates approximately like the system it represents, whereas the solutions of the comparison equation fit approximately those of the original one, but while remaining “on the same side” at any time. One might speak of a one-sided model. The comparison method is sufficiently important in itself to justify the presence here of a complete chapter devoted to this subject. Further, it introduces to some typical applications.

Keywords

Comparison Method Minimum Solution Differential Inequality Maximum Solution Bibliographical Note 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • N. Rouche
    • 1
  • P. Habets
    • 1
  • M. Laloy
    • 1
  1. 1.Institut de Mathématique Pure et AppliquéeU.C.L.Louvain-la-NeuveBelgium

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