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Journal of Applied Mathematics
Volume 2012, Article ID 365904, 14 pages
http://dx.doi.org/10.1155/2012/365904
Research Article

Numerical Solution of Weakly Singular Integrodifferential Equations on Closed Smooth Contour in Lebesgue Spaces

1Department of Mathematics and Statistics, King Faisal University, Saudi Arabia
2Department of Mathematics, Al-Hussein Bin Talal University, P. O. Box 20 Ma'an, Jordan

Received 18 June 2012; Accepted 3 September 2012

Academic Editor: Yongkun Li

Copyright © 2012 Feras M. Al Faqih. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. W. Cohen and O. J. Boxma, Boundary Value Problems in Queueing System Analysis, vol. 79, North-Holland, Amsterdam, The Netherlands, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. A. I. Kalandiya, Mathematical Methods of Two-Dimensional Elasticity, Mir Publishers, Moscow, Russia, 1975. View at Zentralblatt MATH
  3. A. Linkov, Boundary Integral Equations in Elasticity Theory, Kluwer Academic, Dordrecht, The Netherlands, 2002. View at Zentralblatt MATH
  4. N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity. Fundamental Equations, Plane Theory of Elasticity, Torsion and Bending, Noordhoff, Groningen, The Netherlands, 1953. View at Zentralblatt MATH
  5. D. Brockman and L. Hufnagel, “Fronnt propagation in reaction—supper diffusion dynamics: taming lavy flights with fluctuations,” Physical Review Letters, vol. 98, pp. 178311–178314, 2007. View at Google Scholar
  6. E. G. Ladopoulos, Singular Integral Equations: Linear and Non-Linear Theory and Its Applications in Science and Engineering, Springer, New York, NY, USA, 2000.
  7. V. V. Ivanov, The Theory of Approximate Methods and Their Application to the Numerical Solution of Singular Integral Equations, Noordhoff, Leyden, The Netherlands, 1976.
  8. F. D. Gakhov, Boundary Value Problems, Pergamon, Oxford, UK, Addison-Wesley, Reading, Mass, USA, 1966.
  9. N. I. Muskhelishvili, Singular Integral Equations: Boundary Problems of Functions Theory and Their Applications to Mathematical Physics, Noordhoff, Leyden, The Netherlands, 1977.
  10. N. P. Vekua, Systems of Singular Integral Equations, Noordhoff, Groningen, The Netherlands, 1967, Translated from the Russian by A. G. Gibbs and G. M. Simmons.
  11. I. Gohberg and N. Krupnik, Introduction to the Theory of One-Dimensional Singular Integral Operators, Stiintsa, Kishinev, Moldova, 1973, German translation: Birkhause, Basel, Germany, 1979.
  12. S. Prössdorf and B. Silbermann, Numerical Analysis for Integral and Related Operator Equations, Akademie, Berlin, Germany, Birkhauser, Basel, Switzerland, 1991.
  13. S. G. Mikhlin and S. Prössdorf, Singular Integral Operators, vol. 68, Springer, Berlin, Germany, 1986. View at Publisher · View at Google Scholar
  14. S. Prössdorf, Some Classes of Singular Equations, vol. 17, Elsevier, North-Holland, The Netherlands, 1978.
  15. B. Gabdulalhaev, “The polynomial approximations of solution of singular integral and integro-differential equations by Dzyadik,” Izvestia Visshih Ucebhih Zavedenii Mathematics, vol. 6, no. 193, pp. 51–62, 1978 (Russian). View at Google Scholar
  16. V. A. Zolotarevskiĭ, Z. Li, and I. Caraus, “Approximate solution of singular integrodifferential equations by the method of reduction over Faber-Laurent polynomials,” Differential Equation, vol. 40, no. 12, pp. 1764–1769, 2004, translated from Differentsial'nye Uravneniya, vol. 40, no.12, pp. 1682–1686, 2004. View at Google Scholar
  17. I. Caraus, “The numerical solution for systems of singular integro-differential equations by Faber-Laurent polynomials,” in Proceedings of the 3rd international conference on Numerical Analysis and its Applications (NAA '04), vol. 3401 of Lecture notes in Computer Science, pp. 219–223, Springer, New York, NY, USA, 2005.
  18. I. Caraus and F. M. Al Faqih, “Approximate solution of singular integro-differential equations in generalized Holder spaces,” Numerical Algorithms, vol. 45, pp. 205–215, 2007. View at Publisher · View at Google Scholar
  19. V. Zolotarevski, Finite-Dimensional Methods For Solving of Singular Integral Equations on the Closed Contours of Integration, Stiinta, Chisinau, Moldova, 1991.
  20. V. A. Zolotarevskiĭ, “Approximate solution of systems of singular integral equations on some smooth contours in Lp spaces,” Izvestiya Vysshikh Uchebnykh Zavedeniĭ. Matematika, no. 2, pp. 79–82, 1989. View at Google Scholar
  21. Y. Krikunov, “The general boundary Riemann problem and linear singular integrodifferential equation,” The Scientific Notes of the Kazani University, vol. 116, no. 4, pp. 3–29, 1956 (Russian). View at Google Scholar
  22. V. N. Seĭchuk, “Estimates for weakly singular integral operators defined on closed integration contours and their applications to the approximate solution of singular integral equations,” Differential Equations, vol. 41, no. 9, pp. 1311–1322, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. R. Saks, Boundary-Value Problems For Elliptic Systems of Differential Equations, University of Novosibirsk, Novosibirsk, Russia, 1975.
  24. V. I. Smirnov and N. A. Lebedev, Functions of a Complex Variable: Constructive Theory, IIlife, London, UK, 1968, Translated by Scripta Technica.
  25. P. Novati, “A polynomial method based on Fejèr points for the computation of functions of unsymmetric matrices,” Applied Numerical Mathematics, vol. 44, no. 1-2, pp. 201–224, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. V. A. Zolotarevski, “Direct methods for solving singular integral quations on closed smooth contour in spaces Lp,” Revue d'Analyse Numérique et de Théorie de l'Approximation, vol. 25, no. 1-2, pp. 257–265, 1996. View at Google Scholar