On the use of the interpolation polynomial for solutions of singular integral equations
Author:
Steen Krenk
Journal:
Quart. Appl. Math. 32 (1975), 479-484
MSC:
Primary 65R05
DOI:
https://doi.org/10.1090/qam/474919
MathSciNet review:
474919
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Abstract: On the basis of integration of singular integral equations by means of Gaussian quadrature, it is demonstrated how to obtain the corresponding approximate polynomial solution. For some special cases compact formulas are given for the strength of the singularities at the endpoints of the integration interval.
- 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
- F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 29 (1971/72), 525–534. MR 408277, DOI https://doi.org/10.1090/S0033-569X-1972-0408277-4
- 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 448967, DOI https://doi.org/10.1090/S0033-569X-1975-0448967-5
- 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
- N. I. Muskhelishvili, Singular integral equations, Noordhoff International Publishing, Leyden, 1977. Boundary problems of function theory and their application to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted of the 1958 edition. MR 0438058
A. Erdelyi, Higher transcendental functions, Vol. 2, McGraw—Hill, New York, 1953
C. Lanczos, Trigonometric interpolation of empirical and analytical functions, J. Math. Phys. 17, 123 (1938)
C. Lanczos, Applied analysis, Prentice—Hall, New York, 1957
F. Erdogan and G. D. Gupta, Stresses near a flat inclusion in bonded dissimilar materials, Int. J. Solids Structures 8, 533 (1972)
F. Erdogan and M. Ratwani, A circumferential crack in a cylindrical shell under torsion, Int. J. Fracture Mech. 8, 87 (1972)
U. Yuceoglu and F. Erdogan, A cylindrical shell with an axial crack under skew-symmetric loading, Int. J. Solids Structures 9, 347 (1973)
F. Erdogan, Approximate solutions of systems of singular integral equations, SIAM J. Appl. Math. 17, 1041 (1969)
F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 30, 525 (1972)
S. Krenk, On quadrature formulas for singular integral equations of the first and the second kind, Lehigh University, Report IFSM-73-47, August 1973; Quant. Appl. Math., to appear
F. Erdogan, G. D. Gupta and T. S. Cook, Numerical solution of singular integral equations, in Methods of analysis and solutions of crack problems, ed. G. C. Sih, Noordhoff International Publishing, Leyden, 1973
N. I. Muskhelishvili, Singular integral equations, Wolters—Noordhoff Publishing, Groningen, 1958 (see §107)
A. Erdelyi, Higher transcendental functions, Vol. 2, McGraw—Hill, New York, 1953
C. Lanczos, Trigonometric interpolation of empirical and analytical functions, J. Math. Phys. 17, 123 (1938)
C. Lanczos, Applied analysis, Prentice—Hall, New York, 1957
F. Erdogan and G. D. Gupta, Stresses near a flat inclusion in bonded dissimilar materials, Int. J. Solids Structures 8, 533 (1972)
F. Erdogan and M. Ratwani, A circumferential crack in a cylindrical shell under torsion, Int. J. Fracture Mech. 8, 87 (1972)
U. Yuceoglu and F. Erdogan, A cylindrical shell with an axial crack under skew-symmetric loading, Int. J. Solids Structures 9, 347 (1973)
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Article copyright:
© Copyright 1975
American Mathematical Society
