Application of Chebyshew and trigonometric polynomials to the approximation of a solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane

• Autorzy: Karczmarek P.
• Języki publikacji: EN

Abstrakty

EN

In this article Chebyshev and trigonometric polynomials are used to construct an approximate solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane.

Słowa kluczowe

EN

singular integral equation; Cauchy kernel; multiplicative kernel; approximate solution; Chebyshev polynomials; trigonometric polynomials

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 2
• Strony: 129--136
• Opis fizyczny: Bibliogr. 8 poz., tab.

Twórcy

autor

Karczmarek P.

• The John Paul II Catholic University of Lublin, Institute of Mathematics and Computer Science, al. Racławickie 14, 20-950 Lublin, Poland,

Bibliografia

• [1] H. Bateman, A. Erdélyi, Higher Transcendental Functions, vol. 2, McGraw-Hill Book Company, New York, 1953.
• [2] S.M. Belocerkovskii, I.K. Lifanov, Numerical Methods for Singular Integral Equations and its Applications in Aerodynamics, Theory of Elasticity and Electrodynamics, Nauka, Moscow, 1985 [in Russian].
• [3] B.G. Gabdulkhaev, Finite-dimensional approximations of singular integrals and direct methods of solution of singular integral and integrodifferential equations, J. Math. Sci. (N.Y.), 18 (1982) 4, 593–627.
• [4] P. Karczmarek, Singular integral equation with a multiplicative Cauchy kernel in the half-plane, Opuscula Math., 28 (2008), 63–72.
• [5] I.K. Lifanov, Singular Integral Equations and Discrete Vortices, VSP, Amsterdam, 1996.
• [6] S. Paszkowski, Numerical applications of Chebyshev polynomials and series, PWN, Warsaw, 1975 [in Polish].
• [7] D. Pylak, M.A. Sheshko, Inversion of singular integrals with Cauchy kernels in the case of an infinite integration domain, Differ. Equ., 41 (2005), 1297–1310.
• [8] M. Sheshko, Singular Integral Equations with Cauchy and Hilbert Kernels and Theirs Approximated Solutions, The Learned Society of the Catholic University of Lublin, Lublin, 2003.