About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 416757, 8 pages
http://dx.doi.org/10.1155/2013/416757
Research Article

Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials

General Required Courses Department, Jeddah Community College, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 24 April 2013; Accepted 1 September 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 S. H. Behiry. 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. M. Dehghan and A. Saadatmandi, “Chebyshev finite difference method for Fredholm integro-differential equation,” International Journal of Computer Mathematics, vol. 85, no. 1, pp. 123–130, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Z. Lackiewicz, M. Rahman, and B. D. Welfert, “Numerical solution of a Fredholm integro-differential equation modelling neural networks,” Applied Numerical Mathematics, vol. 56, no. 3-4, pp. 423–432, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. Lakestani, M. Razzaghi, and M. Dehghan, “Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations,” Mathematical Problems in Engineering, vol. 2006, Article ID 96184, 12 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. H. Behiry and H. Hashish, “Wavelet methods for the numerical solution of Fredholm integro-differential equations,” International Journal of Applied Mathematics, vol. 11, no. 1, pp. 27–35, 2002. View at Zentralblatt MATH · View at MathSciNet
  5. S. Islam, I. Aziz, and M. Fayyaz, “A new approach for numerical solution of integro-differential equations via Haar wavelets,” International Journal of Computer Mathematics, 2013. View at Publisher · View at Google Scholar
  6. Y. Ordokhani, “An application of Walsh functions for Fredholm-Hammerstein integro-differential equations,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 22, pp. 1055–1063, 2010. View at Zentralblatt MATH · View at MathSciNet
  7. S. Yeganeh, Y. Ordokhani, and A. Saadatmandi, “A sinc-collocation method for second-order boundary value problems of nonlinear integro-differential equation,” Journal of Information and Computing Science, vol. 7, no. 2, pp. 151–160, 2012.
  8. Sh. S. Behzadi, S. Abbasbandy, T. Allahviranloo, and A. Yildirim, “Application of homotopy analysis method for solving a class of nonlinear Volterra-Fredholm integro-differential equations,” The Journal of Applied Analysis and Computation, vol. 2, no. 2, pp. 127–136, 2012. View at MathSciNet
  9. S. H. Behiry and S. I. Mohamed, “Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method,” Natural Science, vol. 4, no. 8, pp. 581–587, 2012.
  10. K. Maleknejad, B. Basirat, and E. Hashemizadeh, “Hybrid Legendre polynomials and block-pulse functions approach for nonlinear Volterra-Fredholm integro-differential equations,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2821–2828, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. Ezzati and S. Najafalizadeh, “Application of Chebyshev polynomials for solving nonlinear Volterra-Fredholm integral equations system and convergence analysis,” Indian Journal of Science and Technology, vol. 5, no. 2, pp. 2060–2064, 2012.
  12. A. H. Bhrawy, E. Tohidi, and F. Soleymani, “A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals,” Applied Mathematics and Computation, vol. 219, no. 2, pp. 482–497, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. Z. H. Jiang and W. Schaufelberger, Block Pulse Functions and Their Applications in Control Systems, Springer, Berlin, Germany, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S. A. Yousefi, Z. Barikbin, and M. Dehghan, “Ritz-Galerkin method with Bernstein polynomial basis for finding the product solution form of heat equation with non-classic boundary conditions,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22, no. 1, pp. 39–48, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  15. K. Maleknejad, E. Hashemizadeh, and B. Basirat, “Computational method based on Bernstein operational matrices for nonlinear Volterra-Fredholm-Hammerstein integral equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 52–61, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. G. Tachev, “Pointwise approximation by Bernstein polynomials,” Bulletin of the Australian Mathematical Society, vol. 85, no. 3, pp. 353–358, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Y. Ordokhani and S. Davaei far, “Application of the Bernstein polynomials for solving the nonlinear Fredholm integro-differential equations,” Journal of Applied Mathematics and Bioinformatics, vol. 1, no. 2, pp. 13–31, 2011.
  18. K. Jalaei, M. Zarebnia, and M. M. Chalaki, “Development of the sinc method for nonlinear integro-differential eequations,” Australian Journal of Basic and Applied Sciences, vol. 4, no. 11, pp. 5508–5515, 2010. View at Scopus