Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 787694, 15 pages
http://dx.doi.org/10.5402/2011/787694
Research Article

Approximate Solutions of Differential Equations by Using the Bernstein Polynomials

Department of Mathematics, Alzahra University, Tehran, Iran

Received 12 March 2011; Accepted 19 April 2011

Academic Editors: F. Ding and G. Psihoyios

Copyright © 2011 Y. Ordokhani and S. Davaei far. 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. B. N. Mandal and S. Bhattacharya, “Numerical solution of some classes of integral equations using Bernstein polynomials,” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1707–1716, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. A. Chakrabarti and S. C. Martha, “Approximate solutions of Fredholm integral equations of the second kind,” Applied Mathematics and Computation, vol. 211, no. 2, pp. 459–466, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. S. Bhattacharya and B. N. Mandal, “Use of Bernstein polynomials in numerical solutions of Volterra integral equations,” Applied Mathematical Sciences, vol. 2, no. 36, pp. 1773–1787, 2008. View at Google Scholar · View at Zentralblatt MATH
  4. M. I. Bhatti and P. Bracken, “Solutions of differential equations in a Bernstein polynomial basis,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 272–280, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. D. D. Bhatta and M. I. Bhatti, “Numerical solution of KdV equation using modified Bernstein polynomials,” Applied Mathematics and Computation, vol. 174, no. 2, pp. 1255–1268, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. K. Singh, V. K. Singh, and O. P. Singh, “The Bernstein operational matrix of integration,” Applied Mathematical Sciences, vol. 3, no. 49, pp. 2427–2436, 2009. View at Google Scholar · View at Zentralblatt MATH
  7. S. A. Yousefi and M. Behroozifar, “Operational matrices of Bernstein polynomials and their applications,” International Journal of Systems Science, vol. 41, no. 6, pp. 709–716, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. S. Bhattacharya and B. N. Mandal, “Numerical solution of a singular integro-differential equation,” Applied Mathematics and Computation, vol. 195, no. 1, pp. 346–350, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. Yousefi, “Legendre wavelets method for solving differential equations of Lane-Emden type,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 1417–1422, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. X. Zheng and X. Yang, “Techniques for solving integral and differential equations by Legendre wavelets,” International Journal of Systems Science, vol. 40, no. 11, pp. 1127–1137, 2009. View at Publisher · View at Google Scholar
  11. M. Razzaghi and S. Yousefi, “Legendre wavelets direct method for variational problems,” Mathematics and Computers in Simulation, vol. 53, no. 3, pp. 185–192, 2000. View at Publisher · View at Google Scholar
  12. A. Golbabai and M. Javidi, “Application of homotopy perturbation method for solving eighth-order boundary value problems,” Applied Mathematics and Computation, vol. 191, no. 2, pp. 334–346, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. M. Mestrovic, “The modified decomposition method for eighth-order boundary value problems,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1437–1444, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. N. Kurt and M. Sezer, “Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients,” Journal of the Franklin Institute, vol. 345, no. 8, pp. 839–850, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. E. Babolian and F. Fattahzadeh, “Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 417–426, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. R. T. Farouki and V. T. Rajan, “Algorithms for polynomials in Bernstein form,” Computer Aided Geometric Design, vol. 5, no. 1, pp. 1–26, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. P. J. Davis, Interpolation and Approximation, Dover, New York, NY, USA, 1975.
  18. E. Isaacson and H. B. Keller, Analysis of Numerical Methods, Dover, New York, NY, USA, 1994.
  19. K. B. Datta and B. M. Mohan, Orthogonal Functions in Systems and Control, World Scientific, River Edge, NJ, USA, 1995.
  20. Y. M. Li and X. Y. Zhang, “Basis conversion among Bezier, Tchebyshev and Legendre,” Computer Aided Geometric Design, vol. 15, no. 6, pp. 637–642, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. R. T. Farouki, “Legendre-Bernstein basis transformations,” Journal of Computational and Applied Mathematics, vol. 119, no. 1-2, pp. 145–160, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. C. H. Hsiao, “Hybrid function method for solving Fredholm and Volterra integral equations of the second kind,” Journal of Computational and Applied Mathematics, vol. 230, no. 1, pp. 59–68, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH