On the numerical solution of singular integral equations
Authors:
F. Erdogan and G. D. Gupta
Journal:
Quart. Appl. Math. 29 (1972), 525-534
MSC:
Primary 65R05
DOI:
https://doi.org/10.1090/qam/408277
MathSciNet review:
408277
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Abstract: In this paper a pair of Gauss-Chebyshev integration formulas for singular integrals are developed. Using these formulas a simple numerical method for solving a system of singular integral equations is described. To demonstrate the effectiveness of the method, a numerical example is given. In order to have a basis of comparison, the example problem is solved also by using an alternate method.
- N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. MR 0355494
- F. D. Gakhov, Boundary value problems, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966. Translation edited by I. N. Sneddon. MR 0198152
- F. Erdogan, Approximate solutions of systems of singular integral equations, SIAM J. Appl. Math. 17 (1969), 1041–1059. MR 261294, DOI https://doi.org/10.1137/0117094
A. Erdelyi (ed.), Higher transcendental functions, Vol. 2, McGraw-Hill, New York, 1953
M. Abramowitz and I. A. Stegun, eds., Handbook of mathematical functions, National Bureau of Standards, Appl. Math. Series 55, 1964
- L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, Interscience Publishers, Inc., New York; P. Noordhoff Ltd., Groningen, 1958. Translated from the 3rd Russian edition by C. D. Benster. MR 0106537
N. Kh. Arutiunian, Contact problem for a half-plane with elastic reinforcement, J. Appl. Math. Mech. (Transl. PMM) 32, 632–646 (1968)
N. I. Muskhelishvili, Singular integral equations, P. Noordhoff Ltd., Groningen, Holland, 1953
F. D. Gakhov, Boundary value problems, Pergamon Press, Oxford, 1966
F. Erdogan, Approximate solutions of systems of singular integral equations, SIAM J. Appl. Math. 17, 1041–1059 (1969)
A. Erdelyi (ed.), Higher transcendental functions, Vol. 2, McGraw-Hill, New York, 1953
M. Abramowitz and I. A. Stegun, eds., Handbook of mathematical functions, National Bureau of Standards, Appl. Math. Series 55, 1964
L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, Interscience, New York, 1958
N. Kh. Arutiunian, Contact problem for a half-plane with elastic reinforcement, J. Appl. Math. Mech. (Transl. PMM) 32, 632–646 (1968)
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Article copyright:
© Copyright 1972
American Mathematical Society
