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Journal of Function Spaces
Volume 2015 (2015), Article ID 758410, 10 pages
http://dx.doi.org/10.1155/2015/758410
Research Article

An Approximation Method for Solving Volterra Integrodifferential Equations with a Weighted Integral Condition

Laboratory of Advanced Materials, Department of Mathematics, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria

Received 19 February 2015; Revised 23 April 2015; Accepted 23 April 2015

Academic Editor: Richard I. Avery

Copyright © 2015 A. Guezane-Lakoud 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. N. Aronszajn, “Theory of reproducing kernels,” Transactions of the American Mathematical Society, vol. 68, pp. 337–404, 1950. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Space in Probability and Statistics, Kluwer Academic, Boston, Mass, USA, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  3. M. Cui and Y. Lin, Nonlinear Numercial Analysis in the Reproducing Kernel Space, Nova Science, New York, NY, USA, 2008.
  4. A. Daniel, Reproducing Kernel Spaces and Applications, vol. 143 of Operator Theory: Advances and Applications, Springer, New York, NY, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  5. C. Minggen and C. Zhong, “How to solve nonlinear operator equation A(v2)+Cv=f,” Applied Mathematics and Computation, vol. 153, no. 2, pp. 403–416, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. Cui and C. Li, “How to solve the equation AuBu+Cu=f,” Applied Mathematics and Computation, vol. 133, no. 2-3, pp. 643–653, 2002. View at Google Scholar
  7. M. Cui and F. Geng, “Solving singular two-point boundary value problem in reproducing kernel space,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 6–15, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. 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 MathSciNet · View at Scopus
  9. M. Cui and Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science Publishers, New York, NY, USA, 2008. View at MathSciNet
  10. H. Du and J. Shen, “Reproducing kernel method of solving singular integral equation with cosecant kernel,” Journal of Mathematical Analysis and Applications, vol. 348, no. 1, pp. 308–314, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. 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 · View at Scopus
  12. 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 · View at Scopus
  13. F. Geng and M. Cui, “Solving singular nonlinear two-point boundary value problems in the reproducing kernel space,” Journal of the Korean Mathematical Society, vol. 45, no. 3, pp. 631–644, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. 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 · View at Scopus
  15. F. Geng and M. Cui, “Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space,” Applied Mathematics and Computation, vol. 192, no. 2, pp. 389–398, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. 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 MathSciNet
  17. J. Li, “A computational method for solving singularly perturbed two-point singular boundary value problem,” International Journal of Mathematical Analysis, vol. 2, no. 21-24, pp. 1089–1096, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Y. Lin, P. Chung, and M. Cui, “A solution of an infinite system of quadratic equations in reproducing kernel space,” Complex Analysis and Operator Theory, vol. 1, no. 4, pp. 571–579, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. Y. Zhou, M. Cui, and Y. Lin, “Numerical algorithm for parabolic problems with non-classical conditions,” Journal of Computational and Applied Mathematics, vol. 230, no. 2, pp. 770–780, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. Y.-l. Wang and L. Chao, “Using reproducing kernel for solving a class of partial differential equation with variable-coefficients,” Applied Mathematics and Mechanics. English Edition, vol. 29, no. 1, pp. 129–137, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. H. Yao and Y. Lin, “New algorithm for solving a nonlinear hyperbolic telegraph equation with an integral condition,” International Journal for Numerical Methods in Biomedical Engineering, vol. 27, no. 10, pp. 1558–1568, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. A. Guezane-Lakoud, N. Bendjazia, and R. Khaldi, “Galerkin method applied to telegraph integro-differential equation with a weighted integral condition,” Boundary Value Problems, vol. 2013, article 102, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. B. Basirat and M. A. Shahdadi, “Solution of nonlinear integro-differential equations with initial conditions by bernstein operational matrix of derivative,” International Journal of Modern Nonlinear Theory and Application, vol. 2, pp. 141–149, 2013. View at Publisher · View at Google Scholar
  24. Z. P. Atabakan, A. K. Nasab, A. Kılıçman, and Z. K. Eshkuvatov, “Numerical solution of nonlinear Fredholm integro-differential equations using spectral homotopy analysis method,” Mathematical Problems in Engineering, vol. 2013, Article ID 674364, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  25. L. Yang and M. Cui, “New algorithm for a class of nonlinear integro-differential equations in the reproducing kernel space,” Applied Mathematics and Computation, vol. 174, no. 2, pp. 942–960, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. 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 · View at Scopus
  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, vol. 2012, Article ID 839836, 16 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  28. 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 · View at Scopus