Table of Contents
ISRN Applied Mathematics
Volume 2013 (2013), Article ID 650467, 7 pages
http://dx.doi.org/10.1155/2013/650467
Research Article

Design Feed Forward Neural Network to Solve Singular Boundary Value Problems

Department of Mathematics, College of Education Ibn Al-Haitham, Baghdad University, Iraq

Received 14 May 2013; Accepted 9 June 2013

Academic Editors: Z. Huang and X. Wen

Copyright © 2013 Luma N. M. Tawfiq and Ashraf A. T. Hussein. 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. S. Agatonovic-Kustrin and R. Beresford, “Basic concepts of artificial neural network (ANN) modeling and its application in pharmaceutical research,” Journal of Pharmaceutical and Biomedical Analysis, vol. 22, no. 5, pp. 717–727, 2000. View at Publisher · View at Google Scholar · View at Scopus
  2. I. E. Lagaris, A. C. Likas, and D. G. Papageorgiou, “Neural-network methods for boundary value problems with irregular boundaries,” IEEE Transactions on Neural Networks, vol. 11, no. 5, pp. 1041–1049, 2000. View at Publisher · View at Google Scholar · View at Scopus
  3. L. N. M. Tawfiq, Design and training artificial neural networks for solving differential equations [Ph.D. thesis], University of Baghdad, College of Education Ibn-Al-Haitham, 2004.
  4. A. Malek and R. Shekari Beidokhti, “Numerical solution for high order differential equations using a hybrid neural network—optimization method,” Applied Mathematics and Computation, vol. 183, no. 1, pp. 260–271, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. Akca, M. H. Al-Lail, and V. Covachev, “Survey on wavelet transform and application in ODE and wavelet networks,” Advances in Dynamical Systems and Applications, vol. 1, no. 2, pp. 129–162, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. S. Mc Fall, An artificial neural network method for solving boundary value problems with arbitrary irregular boundaries [Ph.D. thesis], Georgia Institute of Technology, 2006.
  7. A. Junaid, M. A. Z. Raja, and I. M. Qureshi, “Evolutionary computing approach for the solution of initial value problems in ordinary differential equations,” World Academy of Science, Engineering and Technology, vol. 55, pp. 578–5581, 2009. View at Google Scholar
  8. J. Abdul Samath, P. S. Kumar, and A. Begum, “Solution of linear electrical circuit problem using neural networks,” International Journal of Computer Applications, vol. 2, no. 1, pp. 6–13, 2010. View at Google Scholar
  9. K. I. Ibraheem and B. M. Khalaf, “Shooting neural networks algorithm for solving boundary value problems in ODEs,” Applications and Applied Mathematics, vol. 6, no. 11, pp. 1927–1941, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. A. Hoda I. and H. A. Nagla, “On neural network methods for mixed boundary value problems,” International Journal of Nonlinear Science, vol. 11, no. 3, pp. 312–316, 2011. View at Google Scholar · View at MathSciNet
  11. K. Majidzadeh, “Inverse problem with respect to domain and artificial neural network algorithm for the solution,” Mathematical Problems in Engineering, vol. 2011, Article ID 145608, 16 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. A. Oraibi, Design feed forward neural networks for solving ordinary initial value problem [M.S. thesis], University of Baghdad, College of Education Ibn Al-Haitham, 2011.
  13. M. H. Ali, Design fast feed forward neural networks to solve two point boundary value problems [M.S. thesis], University of Baghdad, College of Education Ibn Al-Haitham, 2012.
  14. I. Rachůnková, S. Staněk, and M. Tvrdý, Solvability of Nonlinear Singular Problems for Ordinary Differential Equations, Hindawi Publishing Corporation, New York, USA, 2008.
  15. L. F. Shampine, J. Kierzenka, and M. W. Reichelt, “Solving Boundary Value Problems for Ordinary Differential Equations in Matlab with bvp4c,” 2000.
  16. H. W. Rasheed, Efficient semi-analytic technique for solving second order singular ordinary boundary value problems [M.S. thesis], University of Baghdad, College of Education Ibn-Al-Haitham, 2011.
  17. A. I. Galushkin, Neural Networks Theory, Springer, Berlin, Germany, 2007. View at MathSciNet
  18. K. Mehrotra, C. K. Mohan, and S. Ranka, Elements of Artificial Neural Networks, Springer, New York, NY, USA, 1996.
  19. A. Ghaffari, H. Abdollahi, M. R. Khoshayand, I. S. Bozchalooi, A. Dadgar, and M. Rafiee-Tehrani, “Performance comparison of neural network training algorithms in modeling of bimodal drug delivery,” International Journal of Pharmaceutics, vol. 327, no. 1-2, pp. 126–138, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. J. I. Ramos, “Piecewise quasilinearization techniques for singular boundary-value problems,” Computer Physics Communications, vol. 158, no. 1, pp. 12–25, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. Kumar, “A three-point finite difference method for a class of singular two-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 145, no. 1, pp. 89–97, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet