Galerkin methods for singular integral equations
Author:
K. S. Thomas
Journal:
Math. Comp. 36 (1981), 193205
MSC:
Primary 65R20; Secondary 45F99
MathSciNet review:
595052
Fulltext PDF Free Access
Abstract 
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Abstract: The approximate solution of a singular integral equation by Galerkin's method is studied. We discuss the theoretical aspects of such problems and give error bounds for the approximate solution.
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 [6]
 M. L. Dow & D. Elliott, "The numerical solution of singular integral equations over ," SIAM J. Numer. Anal., v. 16, 1979, pp. 115134. MR 518688 (80b:65151)
 [7]
 F. Erdogan, G. D. Gupta & T. S. Cook, "Numerical solution of singular integral equations," Mech. Fract., v. 1, 1973, pp. 368425. MR 0471394 (57:11128)
 [8]
 V. V. Ivanov, The Theory of Approximate Methods and Their Applications to the Numerical Solution of Singular Integral Equations, Noordhoff, Leyden, 1976. MR 0405045 (53:8841)
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 L. N. Karpjenko, "Approximate solution of singular integral equations by means of Jacobi polynomials," Prikl. Mat. Meh., v. 30, 1966, pp. 564569; English transl., J. Appl. Math. Mech., v. 30, 1967, pp. 668675. MR 0231156 (37:6711)
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 S. Krenk, "A quadrature formula for singular integral equations of the first and second kind," Quart. Appl. Math., v. 33, 1975, pp. 225232. MR 0448967 (56:7272)
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 P. Linz, "A general theory for the approximate solution of operator equations of the second kind," SIAM J. Numer. Anal., v. 14, 1977, pp. 543553. MR 0431665 (55:4660)
 [12]
 N. I. Mushkhelishvili, Singular Integral Equations, Noordhoff, Groningen, 1953.
 [13]
 J. R. Rice, "On the degree of convergence of nonlinear spline approximation," Approximation with Special Emphasis on Spline Functions (I. J. Schoenberg, Ed.), Academic Press, New York, 1969, pp. 349365. MR 0267324 (42:2226)
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 K. S. Thomas, "On the approximate solution of operator equations," Numer. Math., v. 23, 1975, pp. 231239. MR 0373275 (51:9475)
 [15]
 F. G. Tricomi, Integral Equations, Pure and Appl. Math., vol. 5, Interscience, New York, 1957. MR 0094665 (20:1177)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198105950529
PII:
S 00255718(1981)05950529
Article copyright:
© Copyright 1981 American Mathematical Society
