Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Galerkin methods for singular integral equations


Author: K. S. Thomas
Journal: Math. Comp. 36 (1981), 193-205
MSC: Primary 65R20; Secondary 45F99
MathSciNet review: 595052
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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

  • [1] Carl de Boor, Good approximation by splines with variable knots, Spline functions and approximation theory (Proc. Sympos., Univ. Alberta, Edmonton, Alta., 1972), Birkhäuser, Basel, 1973, pp. 57–72. Internat. Ser. Numer. Math., Vol. 21. MR 0403169 (53 #6982)
  • [2] Hermann G. Burchard, Splines (with optimal knots) are better, Applicable Anal. 3 (1973/74), 309–319. MR 0399708 (53 #3551)
  • [3] T. Carleman, "Sur la résolution de certaines équations intégrales," Ark. Mat. Astronom. Fys., v. 16, 1921, pp. 1-19.
  • [4] Y. Cherruault, Approximation d’opérateurs linéaires et applications, Monographies d’informatique, No. 4, Dunod, Paris, 1968 (French). MR 0236584 (38 #4879)
  • [5] D. S. Dodson, Optimal Order Approximation by Polynomial Spline Functions, Ph. D. Thesis, Comp. Sci. Dept., Purdue Univ., Lafayette, Ind., 1972.
  • [6] M. L. Dow and David Elliott, The numerical solution of singular integral equations over (-1,1), SIAM J. Numer. Anal. 16 (1979), no. 1, 115–134. MR 518688 (80b:65151), http://dx.doi.org/10.1137/0716009
  • [7] F. Erdogan, G. D. Gupta, and T. S. Cook, Numerical solution of singular integral equations, Mechanics of fracture, Vol. 1, Noordhoff, Leiden, 1973, pp. 368–425. MR 0471394 (57 #11128)
  • [8] V. V. Ivanov, The theory of approximate methods and their application to the numerical solution of singular integral equations, Noordhoff International Publishing, Leyden, 1976. Translated from the Russian by A. Ideh; Edited by R. S. Anderssen and D. Elliott; Monographs and Textbooks on Mechanics of Solids and Fluids, Mechanics: Analysis, No. 2. MR 0405045 (53 #8841)
  • [9] L. N. Karpenko, Approximation solution of a singular integral equation by means of Jacobi polynomials, J. Appl. Math. Mech. 30 (1966), 668–675. MR 0231156 (37 #6711)
  • [10] Steen Krenk, On quadrature formulas for singular integral equations of the first and the second kind, Quart. Appl. Math. 33 (1975/76), no. 3, 225–232. MR 0448967 (56 #7272)
  • [11] Peter Linz, A general theory for the approximate solution of operator equations of the second kind, SIAM J. Numer. Anal. 14 (1977), no. 3, 543–554. MR 0431665 (55 #4660)
  • [12] N. I. Mushkhelishvili, Singular Integral Equations, Noordhoff, Groningen, 1953.
  • [13] John R. Rice, On the degree of convergence of nonlinear spline approximation, Approximations with Special Emphasis on Spline Functions (Proc. Sympos. Univ. of Wisconsin, Madison, Wis., 1969), Academic Press, New York, 1969, pp. 349–365. MR 0267324 (42 #2226)
  • [14] K. S. Thomas, On the approximate solution of operator equations, Numer. Math. 23 (1974/75), 231–239. MR 0373275 (51 #9475)
  • [15] F. G. Tricomi, Integral equations, Pure and Applied Mathematics. Vol. V, Interscience Publishers, Inc., New York, 1957. MR 0094665 (20 #1177)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R20, 45F99

Retrieve articles in all journals with MSC: 65R20, 45F99


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0595052-9
PII: S 0025-5718(1981)0595052-9
Article copyright: © Copyright 1981 American Mathematical Society