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Rational and Algebraic Approximation for Initial- and Boundary-Value-Problems

  • Lothar Collatz
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 90)

Abstract

There are boundary value problems with unbounded domains for which it is better to approximate the wanted solution by rational functions than by polynomials. Sometimes it may be necessary to use even more complicated approximations, for instance algebraic approximations. In simple cases it is possible to give guaranteeable inclusions for the solutions if monotonicity principles are valued. Some numerical examples are given.

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References

  1. L. Collatz (1981): Anwendung von Monotoniesätzen zur Einschliessung der Lösungen von Gleichungen. Jahrbuch Überblicke der Mathem., 189–225.Google Scholar
  2. L. Collatz (1988): Inclusion of solutions of some singular boundary value problems in two and three dimensions. Intern. Ser. Numer. Mathem., Vol. 86, Birkhäuser, 115–125.Google Scholar
  3. G. Meinardus (1967): Approximation of functions, theory and numerical methods, Springer, 198 p. J. Schröder (1980): Operator inequalitites, Acad. Press. 367 p.Google Scholar
  4. H. Werner (1962): Konstruktive Ermittlung der Tschebyscheff-Approximierenden im Bereich der rationalen Funktionen. Arch. Rat. Mech. Anal. 11, 368–384.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • Lothar Collatz
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HamburgHamburg 13Federal Republic of Germany

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