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Mathematical Problems in Engineering
Volume 2013, Article ID 832074, 10 pages
http://dx.doi.org/10.1155/2013/832074
Research Article

A Computational Method for Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential Equations

1Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan
2Department of Mathematics, Al-Balqa Applied University, Salt 19117, Jordan
3Department of Mathematics, University of Jordan, Amman 11942, Jordan

Received 27 July 2012; Accepted 29 January 2013

Academic Editor: Hung Nguyen-Xuan

Copyright © 2013 Mohammed Al-Smadi et al. 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. F. Bloom, “Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory,” Journal of Mathematical Analysis and Applications, vol. 73, no. 2, pp. 524–542, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  2. K. Holmåker, “Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones,” SIAM Journal on Mathematical Analysis, vol. 24, no. 1, pp. 116–128, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. L. K. Forbes, S. Crozier, and D. M. Doddrell, “Calculating current densities and fields produced by shielded magnetic resonance imaging probes,” SIAM Journal on Applied Mathematics, vol. 57, no. 2, pp. 401–425, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. P. Kanwal, Linear Integral differential Equations Theory and Technique, Academic Press, New York, NY, USA, 1971.
  5. A.-M. Wazwaz, “A reliable algorithm for solving boundary value problems for higher-order integro-differentiable equations,” Applied Mathematics and Computation, vol. 118, no. 2-3, pp. 327–342, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. Arikoglu and I. Ozkol, “Solution of boundary value problems for integro-differential equations by using differential transform method,” Applied Mathematics and Computation, vol. 168, no. 2, pp. 1145–1158, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. Yıldırım, “Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method,” Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3175–3180, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Saeidy, M. Matinfar, and J. Vahidi, “Analytical solution of BVPs for fourth-order integro-differential equations by using homotopy analysis method,” International Journal of Nonlinear Science, vol. 9, no. 4, pp. 414–421, 2010. View at Google Scholar · View at MathSciNet
  9. O. Abu Arqub, “Series solution of fuzzy differential equations under strongly generalized di erentiability,” Journal of Advanced Research in Applied Mathematics, vol. 5, pp. 31–52, 2013. View at Google Scholar
  10. O. Abu Arqub, A. El-Ajou, S. Momani, and N. Shawagfeh, “Analytical solutions of fuzzy initial value problems by HAM,” Applied Mathematics and Information Sciences. In press.
  11. O. Abu Arqub and A. El-Ajou, “Solution of the fractional epidemic model by homotopy analysis method,” Journal of King Saud University (Science), vol. 25, pp. 73–81, 2013. View at Google Scholar
  12. S. Momani and R. Qaralleh, “An efficient method for solving systems of fractional integro-differential equations,” Journal of Mathematical Analysis and Applications, vol. 52, no. 3-4, pp. 459–470, 2006. View at Publisher · View at Google Scholar
  13. A. El-Ajou, O. Abu Arqub, and S. Momani, “Homotopy analysis method for second-order boundary value problems of integro-differential equations,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 365792, 18 pages, 2012. View at Publisher · View at Google Scholar
  14. O. Abu Arqub, Z. Abo-Hammour, and S. Momani, “Application of continuous genetic algorithm for nonlinear system of second-order boundary value problems,” Applied Mathematics and Information Sciences. In press.
  15. O. Abu Arqub, Z. Abo-Hammour, S. Momani, and N. Shawagfeh, “Solving singular two-point boundary value problems using continuous genetic algorithm,” Abstract and Applied Analysis, vol. 2012, Article ID 205391, 25 pages, 2012. View at Publisher · View at Google Scholar
  16. A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics, Kluwer Academic Publishers, Boston, Mass, USA, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  17. M. Cui and Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science, New York, NY, USA, 2009. View at MathSciNet
  18. D. Alpay, Ed., Reproducing Kernel Spaces and Applications, vol. 143 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  19. C.-l. Li and M.-g. Cui, “The exact solution for solving a class nonlinear operator equations in the reproducing kernel space,” Applied Mathematics and Computation, vol. 143, no. 2-3, pp. 393–399, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. F. Geng and M. Cui, “Solving a nonlinear system of second order boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 1167–1181, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. F. Geng, “A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems,” Applied Mathematics and Computation, vol. 213, no. 1, pp. 163–169, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. Y. Li, F. Geng, and M. Cui, “The analytical solution of a system of nonlinear differential equations,” International Journal of Mathematical Analysis, vol. 1, no. 9–12, pp. 451–462, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. F. Geng, “Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method,” Applied Mathematics and Computation, vol. 215, no. 6, pp. 2095–2102, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Y. Z. Lin, M. G. Cui, and L. H. Yang, “Representation of the exact solution for a kind of nonlinear partial differential equation,” Applied Mathematics Letters, vol. 19, no. 8, pp. 808–813, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. Cui and H. Du, “Representation of exact solution for the nonlinear Volterra-Fredholm integral equations,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1795–1802, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. M. Al-Smadi, O. Abu Arqub, and N. Shawagfeh, “Approximate solution of BVPs for 4th-order IDEs by using RKHS method,” Applied Mathematical Sciences, vol. 6, no. 49–52, pp. 2453–2464, 2012. View at Google Scholar · View at MathSciNet
  27. O. Abu Arqub, M. Al-Smadi, and S. Momani, “Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integrodifferential equations,” Abstract and Applied Analysis, Article ID 839836, 16 pages, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet