Numerische Mathematik

, Volume 32, Issue 4, pp 381–392 | Cite as

Pointwise inclusions of fixed points by finite dimensional iteration schemes

  • Jürgen Sprekels
  • Heinrich Voss


Finite dimensional iteration schemes which provide pointwise bounds for the solutions of nonlinear integral equations are considered. The method is based on a discretization technique which takes advantage of apriori known structure properties of the solutions. The resulting iteration can be carried out on a computer for as many steps as desired. Its high degree of accuracy is shown by numerical examples.

Subject Classifications

AMS(MOS) 65R05 


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  1. 1.
    Amann, H.: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces. SIAM Review18, 620–709 (1976)Google Scholar
  2. 2.
    Chandrasekhar, S.: The Transfer of Radiation in Stellar Atmospheres. Bull. Amer. Math. Soc.53, 647–711 (1947)Google Scholar
  3. 3.
    Collatz, L.: Funktionalanalysis und Numerische Mathematik, 2nd Ed., Berlin-New York-Heidelberg: Springer, 1968Google Scholar
  4. 4.
    Leggett, R.W.: On Certain Nonlinear Integral Equations. J. Math. Anal. Appl.57, 462–468 (1977)Google Scholar
  5. 5.
    Protter, M.H., Weinberger, H.F.: Maximum Principles in Differential Equations. Prentice-Hall, Englewood Cliffs 1967Google Scholar
  6. 6.
    Schröder, J.: Anwendung von Fixpunktsätzen bei der numerischen Behandlung nichtlinearer Gleichungen in halbgeordneten Räumen. Arch. Rat. Mech. Anal.4, 177–192 (1960)Google Scholar
  7. 7.
    Sprekels, J.: Finite Dimensional Cone Iteration Techniques for Superlinear Hammerstein Equations. To appear in: Numerical Functional Analysis and OptimizationGoogle Scholar
  8. 8.
    Werner, B.: Monotonie und finite Elemente bei elliptischen Differentialgleichungen. Intern. Ser. Numer. Math. 27, 309–329, Birkhäuser Verlag, Basel-Stuttgart 1975Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Jürgen Sprekels
    • 1
  • Heinrich Voss
    • 1
  1. 1.Institut für Angewandte Mathematik der Universität HamburgHamburg 13Bundesrepublik Deutschland

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