Abstract
We establish convergence rates for a method of approximate solution of certain singular integral equations. The method considered involves an expansion of the kernel of the equation in terms of Chebyshev polynomials.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Brakhage, Bemerkung zur numerischen Behandlung und Fehlerabschätzung bei singularen Integralgleichungen, Zeitschr. f. Angew. Math. Mech. 41 (1961), T12-T14.
F. Erdogan,Approximate solution of systems of singular integral equations, SIAM J. Appl. Math. 17 (1969), 1041–1059.
F. Erdogan and G. D. Gupta,On the numerical solution of singular integral equations, Quart. Appl. Math. 30 (1972), 525–534.
S Krenk,On quadrature formulas for singular integral equations of the first and second kinds, Quart. Appl. Math. 33 (1975), 225–232.
N. I. Muskelishvili,Singular Integral Equations, Nordhoff, Groningen 1953.
T. J. Rivlin,An Introduction to the Approximation of Functions, Blaisdell Publ. Co., Waltham, Mass. 1969.
M. Schleiff, Über Näherungsverfahren zur Lösung einer singulären linearen Integro-differentialgleichung, Zeitschr. f. Angew. Math. Mech. 48 (1968), 477–486.
F. G. Tricomi,Integral Equations, Interscience, New York 1957.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Linz, P. An analysis of a method for solving singular integral equations. BIT 17, 329–337 (1977). https://doi.org/10.1007/BF01932153
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01932153