Further convergence results for the weighted Galerkin method of numerical solution of Cauchytype singular integral equations
Author:
N. I. Ioakimidis
Journal:
Math. Comp. 41 (1983), 7985
MSC:
Primary 65R20; Secondary 45E05, 45L10
MathSciNet review:
701625
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Abstract: The convergence of the weighted Galerkin method (based on Chebyshev or Jacobi polynomials) for the direct numerical solution of onedimensional, real Cauchytype singular integral equations of the first and of the second kind on a finite interval is proved under sufficiently weak continuity assumptions for the kernels and the rightside functions of the integral equations.
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 K. E. Atkinson, A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind, SIAM, Philadelphia, Pennsylvania, 1976. MR 0483585 (58:3577)
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 [5]
 F. Erdogan, G. D. Gupta & T. S. Cook, "Numerical solution of singular integral equations," Mechanics of Fracture, v. 1: Methods of Analysis and Solutions of Crack Problems (G. C. Sih, ed.), Ch. 7, pp. 368425, Noordhoff, Leyden, The Netherlands, 1973. MR 0471394 (57:11128)
 [6]
 J. A. Fromme & M. A. Golberg, "Numerical solution of a class of integral equations arising in twodimensional aerodynamics," in Solution Methods for Integral Equations (M. A. Golberg, ed.), Ch. 4, pp. 109163, Plenum Press, New York, 1979. MR 564266 (81a:65120)
 [7]
 F. D. Gakhov, Boundary Value Problems, Pergamon Press and AddisonWesley, Oxford, 1966. MR 0198152 (33:6311)
 [8]
 M. A. Golberg, "Galerkin's method for operator equations with nonnegative indexwith application to Cauchy singular integral equations," J. Math. Anal. Appl. (To appear.)
 [9]
 N. I. Ioakimidis, "On the weighted Galerkin method of numerical solution of Cauchy type singular integral equations," SIAM J. Numer. Anal., v. 18, 1981, pp. 11201127. MR 639002 (82k:65083)
 [10]
 S. Krenk, "On quadrature formulas for singular integral equations of the first and the second kind," Quart. Appl. Math., v. 33, 1975, pp. 225232. MR 0448967 (56:7272)
 [11]
 P. Linz, "An analysis of a method for solving singular integral equations," BIT, v. 17, 1977, pp. 329337. MR 0483594 (58:3586)
 [12]
 T. J. Rivlin, An Introduction to the Approximation of Functions, Blaisdell, Waltham, Mass., 1969. MR 0249885 (40:3126)
 [13]
 G. Szegö, Orthogonal Polynomials, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1959.
 [14]
 K. S. Thomas, "Galerkin methods for singular integral equations," Math. Comp., v. 36, 1981, pp. 193205. MR 595052 (82c:65092)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198307016254
PII:
S 00255718(1983)07016254
Article copyright:
© Copyright 1983 American Mathematical Society
