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Closed-form expressions for certain induction integrals involving Jacobi and Chebyshev polynomials. (English) Zbl 0941.65134

In the numerical solution of Cauchy singular integral equations (applied in airfoil theory, elasticity, and hydrodynamics) by collocation methods, certain non-singular mutual-induction integrals involving Jacobi and Chebyshev polynomials appear. However, the corresponding recursion scheme is seriously corrupted by numerical noise. The author shows that it is possible to derive closed-form expressions for these integrals that are free of such problems.

MSC:

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

[1] M. A. Golberg, Introduction to the numerical solution of Cauchy singular integral equations, in, Numerical Solution of Integral Equations, edited by, M. A. Golberg, Plenum, New York, 1990.; M. A. Golberg, Introduction to the numerical solution of Cauchy singular integral equations, in, Numerical Solution of Integral Equations, edited by, M. A. Golberg, Plenum, New York, 1990. · Zbl 0735.65092
[2] E. O. Tuck, Application and solution of Cauchy singular integral equations, in, The Application and Numerical Solution of Integral Equations, edited by, R. S. Anderssen, F. R. deHoog, and M. A, Lukas, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980.; E. O. Tuck, Application and solution of Cauchy singular integral equations, in, The Application and Numerical Solution of Integral Equations, edited by, R. S. Anderssen, F. R. deHoog, and M. A, Lukas, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980. · Zbl 0451.76012
[3] Muskhelishvili, N. I., Singular Integral Equations (1953) · Zbl 0051.33203
[4] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1965) · Zbl 0515.33001
[5] Szegö, G., Orthogonal Polynomials (1939) · JFM 65.0278.03
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