Approximate solutions of a singular integral equation with Cauchy kernels in the quarter plane

• Autorzy: Pylak D.
• Języki publikacji: EN

Abstrakty

EN

In the paper, we present explicit formulae for the solution of the singular integral equation with Cauchy kernels in the quarter plane. Next, Jacobi and Chebyshev polynomials are used to derive approximate solutions of this equation.

Słowa kluczowe

EN

singular integral equation; Cauchy kernel; Chebyshev and Jacobi polynomials

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 2
• Strony: 179--194
• Opis fizyczny: Bibliogr. 11 poz., tab.

Twórcy

autor

Pylak D.

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

Bibliografia

• [1] R. Estrada, R.P. Kanwal, Singular integral equations, Birkhäuser, Boston, 2000.
• [2] F.D. Gakhov, Boundary Value Problems, International Series of Monographs in Pure and Applied Mathematics, Vol. 85, Pregamon Press, Oxford, 1966.
• [3] P. Karczmarek, D. Pylak, M. Sheshko, Application of Jacobi polynomials to approximate solution of a singular integral equation with Cauchy kernel, Applied Mathematics and Computation, 181 (2006), 694–707.
• [4] J.C. Mason, D.C. Handscomb, Chebyshev Polynomials, Chapman and Hall/CRC, 2003.
• [5] N.I. Muskhelishvilli, Singular Integral Equations, Nauka, Moscow, 1968 [in Russian].
• [6] S. Paszkowski, Numerical Applications of Chebyshev Polynomials and Series, PWN, Warsaw, 1975.
• [7] D. Pylak, M.A. Sheshko, Inversion of singular integrals with Cauchy kernels in the case of an infinite integration domain, Differential Equations, 41 (2005) 9.
• [8] D. Pylak, Application of Jacobi polynomials to the approximate solution of a singular integral equation with Cauchy kernel on the real half-line, Computational Methods in Applied Mathematics, 6 (2006) 3, 1–10.
• [9] M. Sheshko, Singular Integral Equations with Cauchy and Hilbert Kernels and Theirs Appoximated Solutions, The Learned Society of the Catholic University of Lublin, Lublin, 2003.
• [10] R. Smarzewski, M.A. Sheshko, G.A. Rasolko, Orthogonal approximate solution of Cauchy-type singular integral equations, Computational Methods in Applied Mathematics, 1 (2001) 1, 1–26.
• [11] G. Szegö, Orthogonal polynomials, American Mathematical Society, Colloquium Publications, Vol. XXIII, 1939.