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Global solution of the generalized Abel integral equation by implicit interpolation

Author: H. Brunner
Journal: Math. Comp. 28 (1974), 61-67
MSC: Primary 65R05
MathSciNet review: 0331830
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Abstract: The construction of a (global) approximate solution for a given generalized Abel integral equation may be viewed as a problem of (implicit) interpolation in a prescribed linear space. In this paper, piecewise polynomials (extended spline functions) of a given degree and of class C are used to generate such an approximating function. Results on convergence and error bounds are given, and the practical application of this method is illustrated by a numerical example.

References [Enhancements On Off] (What's this?)

  • [1] M. Bôcher, An Introduction to the Study of Integral Equations, 2nd ed., Cambridge Univ. Press, London, 1914.
  • [2] H. Brunner, "The numerical solution of the generalized Abel integral equation by piecewise polynomials," Notices Amer. Math. Soc., v. 19, 1972, p. A-662. (Abstract)
  • [3] M. G. Cox, "Curve fitting with piecewise polynomials," J. Inst. Math. Appl., v. 8, 1971, pp. 36-52. MR 44 #4870. MR 0287667 (44:4870)
  • [4] P. J. Davis, Interpolation and Approximation, Blaisdell, New York, 1963. MR 28 #393. MR 0157156 (28:393)
  • [5] P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962. MR 24 #B1772. MR 0135729 (24:B1772)
  • [6] A. Huber, "Eine Näherungsmethode zur Auflösung Volterrascher Integralgleichungen," Monatsh. Math. Phys., v. 47, 1939, pp. 240-246. MR 1550815
  • [7] R. Weiss, "Product integration for the generalized Abel equation," Math. Comp., v. 26, 1972, pp. 177-190. MR 45 #8050. MR 0299001 (45:8050)
  • [8] R. Weiss & R. S. Anderssen, "A product integration method for a class of singular first kind Volterra equations," Numer. Math., v. 18, 1972, pp. 442-456. MR 0312759 (47:1314)

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Keywords: Implicit interpolation, generalized Abel integral equation, continuous approximate solution, piecewise polynomials
Article copyright: © Copyright 1974 American Mathematical Society

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