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Abel’s Integral Equation

  • Wolfgang Hackbusch
Chapter
  • 553 Downloads
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 120)

Abstract

The following Volterra integral equation of the first kind is due to Abel (1823):
$$g(x) = \int\limits_a^x {\frac{{f(y)}} {{\sqrt {x - y} }}dy\;for\;x \geqslant a}$$
(6.1.1)
. Since the denominator \(\sqrt {x - y} \) has a zero at y=x, the integral in (1) is to be understood in the improper sense (cf. §6.1.3) and Abel’s integral equation is an example of a weakly singular equation.

Keywords

Integral Equation Quadrature Formula Integral Sign Volterra Integral Equation Integral Equa 
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

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielKielGermany

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