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Ioakimidis, N. I.; Theocaris, P. S.

On convergence of two direct methods for solution of Cauchy type singular integral equations of the first kind. (English) Zbl 0426.65072

BIT, Nord. Tidskr. Inf.-behandl. 20, 83-87 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0426.65072

Cited in 15 Documents

MSC:

65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type

Keywords:

convergence; direct methods; Cauchy type singular integral equations; first kind; Gauss-Chebyshev or Lobatto-Chebyshev numerical integration
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References:

[1] F. Erdogan,Approximate solution of systems of singular integral equations, SIAM J. Appl. Math. 17 (1969), 1041–1059. · Zbl 0187.12404 · doi:10.1137/0117094
[2] F. Erdogan and G. D. Gupta,On the numerical solution of singular integral equations, Quart. Appl. Math. 29 (1972), 525–534. · Zbl 0236.65083 · doi:10.1090/qam/408277
[3] L. Fox and I. B. Parker,Chebyshev Polynomials in Numerical Analysis, 2nd ed., Oxford University Press, London 1972.
[4] N. I. Ioakimidis and P. S. Theocaris,On the numerical evaluation of Cauchy principal value integrals, Rev. Roumaine Sci, Tech. Sér, Méc. Appl. 22 (1977), 803–818. · Zbl 0376.65009
[5] Z. Kopal,Numerical Analysis, Chapman & Hall, London 1961.
[6] P. Linz,An analysis of a method for solving singular integral equations, BIT 17 (1977), 329–337. · Zbl 0372.65057 · doi:10.1007/BF01932153
[7] Y. L. Luke,Mathematical Functions and Their Approximations, Academic Press, New York 1975. · Zbl 0318.33001
[8] T. J. Rivlin,The Chebyshev Polynomials, Wiley-Interscience, New York 1974. · Zbl 0299.41015
[9] P. S. Theocaris and N. I. Ioakimidis,Numerical integration methods for the solution of singular integral equations, Quart. Appl. Math. 35 (1977), 173–183. · Zbl 0353.45016 · doi:10.1090/qam/445873
[10] P. S. Theocaris and N. I. Ioakimidis,A remark on the numerical solution of singular integral equations and the determination of stress-intensity factors, J. Engrg Math. 13 (1979), 213–222. · Zbl 0404.73080 · doi:10.1007/BF00036670
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