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Chebyshev Polynomials for Solving a Class of Singular Integral Equations
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
Department of Mathematics, Faculty of Science and Arts Al-Mithnab, Qassim University, Qassim, KSA
- 1 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
- 2 Department of Mathematics, Faculty of Science and Arts Al-Mithnab, Qassim University, Qassim, KSA
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Abstract
This paper is devoted to studying the approximate solution of singular integral equations by means of Chebyshev polynomials. Some examples are presented to illustrate the method.
KeywordsSingular Integral EquationsCauchy KernelChebyshev PolynomialsWeight Functions
- Chakrabarti, A. (1989) Solution of Two Singular Integral Equations Arising in Water Wave Problems. ZAMM, 69, 457-459. http://dx.doi.org/10.1002/zamm.19890691209
- Ladopoulous, E.G. (2000) Singular Integral Equations Linear and Non-Linear Theory and Its Applications in Science and Engineering. Springer, Berlin.
- Ladopoulous, E.G. (1987) On the Solution of the Two-Dimensional Problem of a Plane Crack of Arbitrary Shape in an Anisotropic Material. Engineering Fracture Mechanics, 28, 187-195. http://dx.doi.org/10.1016/0013-7944(87)90212-8
- Zabreyko, P.P. (1975) Integral Equations—A Reference Text. Noordhoff, Leyden. http://dx.doi.org/10.1007/978-94-010-1909-5
- Prossdorf, S. (1977) On Approximate Methods for the Solution of One-Dimensional Singular Integral Equations. Applicable Analysis, 7, 259-270.
- Zisis, V.A. and Ladopoulos, E.G. (1989) Singular Integral Approximations in Hilbert Spaces for Elastic Stress Analysis in a Circular Ring with Curvilinear Cracks. Indus. Math., 39, 113-134.
- Chakrabarti, A. and Berghe, V.G. (2004) Approximate Solution of Singular Integral Equations. Applied Mathematics Letters, 17, 553-559. http://dx.doi.org/10.1016/S0893-9659(04)90125-5
- Abdou, M.A. and Naser, A.A. (2003) On the Numerical Treatment of the Singular Integral Equation of the Second Kind. Applied Mathematics and Computation, 146, 373-380. http://dx.doi.org/10.1016/S0096-3003(02)00587-8
- Abdulkawi, M., Eshkuvatov, Z.K. and Nik Long, N.M.A. (2009) A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type. International Journal of Applied Mathematics and Computer Science, 5, 90-93.
- Eshkuvatov, Z.K., Nik Long, N.M.A. and Abdulkawi, M. (2009) Approximate Solution of Singular Integral Equations of the First Kind with Cauchy Kernel. Applied Mathematics Letters, 22, 651-657. http://dx.doi.org/10.1016/j.aml.2008.08.001
- Gakhov, F.D. (1966) Boundary Value Problems. Addison-Wesley, Boston.
- Martin, P.A. and Rizzo, F.J. (1989) On Boundary Integral Equations for Crack Problems. Proceedings of the Royal Society A, 421, 341-345. http://dx.doi.org/10.1098/rspa.1989.0014
- Sheshko, M. (2003) Singular Integral Equations with Cauchy and Hilbert Kernels and Their Approximated Solutions. The Learned Society of the Catholic University of Lublin, Lublin. (in Russian)