Global solution of the generalized Abel integral equation by implicit interpolation
Author:
H. Brunner
Journal:
Math. Comp. 28 (1974), 6167
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.
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 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. A662. (Abstract)
 [3]
 M. G. Cox, "Curve fitting with piecewise polynomials," J. Inst. Math. Appl., v. 8, 1971, pp. 3652. 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. 240246. MR 1550815
 [7]
 R. Weiss, "Product integration for the generalized Abel equation," Math. Comp., v. 26, 1972, pp. 177190. 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. 442456. MR 0312759 (47:1314)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403318305
PII:
S 00255718(1974)03318305
Keywords:
Implicit interpolation,
generalized Abel integral equation,
continuous approximate solution,
piecewise polynomials
Article copyright:
© Copyright 1974
American Mathematical Society
