An Adaptive Step Size Control for Volterra Integral Equations

  • Herbert Arndt
Part of the International Series of Numerical Mathematics book series (ISNM, volume 73)

Abstract

Consider the Volterra integral equation of the second kind
$$y(x) = f(x) + \int\limits_a^x {K(x,t,y(t))dt,{\text{ x}} \in \left[ {{\text{a,b}}} \right]} $$
with continuous f and continuous kernel K.

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References

  1. 1.
    Arndt,H., On Step Size Control for Volterra Integral Equations, in: Collatz, L., Meinardus,G., Werner,H., Numerical Methods of Approximation Theory, ISNM 67, Birkhauser-Verlag, Basel (1983), 9–17.Google Scholar
  2. 2.
    Baker, C.T.H., The Numerical Treatment of Integral Equations, Clarendon Press, Oxford (1977).Google Scholar
  3. 3.
    Brunner,H., Hairer,E., N0rsett,S.P., Runge-Kutta Theory for Volterra Integral Equations of the Second Kind, Mathematics of Computation 39 (1982), 147–163.CrossRefGoogle Scholar
  4. 4.
    Hairer.E., Lubich,Ch., Norsett,S.P., Order of One-Step Methods for Volterra Integral Equations of the Second Kind, SIAM J. Numer. Anal. 20 (1983), 569–579.CrossRefGoogle Scholar
  5. 5.
    Kunkel,P., Ein adaptives Verfahren zur Losung von Volterraschen Integralgleichungen zweiter Art, Diplomarbeit, Heidelberg (1982).Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1985

Authors and Affiliations

  • Herbert Arndt
    • 1
  1. 1.Institut für Angewandte Mathematik der Universität BonnBonnGermany

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