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On the approximate solution of first-kind integral equations of Volterra type

Über die numerische Lösung Volterrascher Integralgleichungen erster Art

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Abstract

The present paper deals with the approximate solution of integral equations of the first kind, (

y)x∈I:=[a, b], where

denotes a (linear) integral operator of Volterra (or Abel) type, and whereg∈C(I), withg(a)=0. The given functiong is approximated uniformly onI (or on a finite subsetZ⊂I by using certain weak Chebyshev systems onI which are obtained in a natural way. By the linearity of

this yields an approximation to the exact solutiony onI. Questions of uniqueness and characterization of such approximating functions, as well as numerical aspects of the approximation problem are discussed.

Zusammenfassung

Die vorliegende Arbeit behandelt die numerische Lösung von Integralgleichungen erster Art, nämlich (

y)x∈I:=[a, b], mitg∈C(I), g(a)=0, wobei

ein (linearer) Integraloperator vom Volterraschen (oder Abelschen) Typ bezeichnet. Die gegebene Funktiong wird aufI (oder auf einer endlichen TeilmengeZ⊂I) unter Benutzung gewisser schwacher (weak) Tschebyscheff-Systeme gleichmäßig angenähert. Wegen der Linearität von

besitzt man daher sofort eine Näherungsfunktion für die gesuchte Lösungy. Die Existenz und Charakterisierung wie auch die numerische Bestimmung solcher Näherungsfunktionen wird untersucht.

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Author notes

  1. H. Brunner

    Present address: Department of Mathematics, University of Dundee, Dundee, Scotland

Authors and Affiliations

  1. Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada

    H. Brunner

Authors
  1. H. Brunner
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Additional information

This research was supported by the National Research Council of Canada (Grant No. A-4805).

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Brunner, H. On the approximate solution of first-kind integral equations of Volterra type. Computing 13, 67–79 (1974). https://doi.org/10.1007/BF02268392

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  • DOI: https://doi.org/10.1007/BF02268392

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