Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 351764, 10 pages
http://dx.doi.org/10.1155/2012/351764
Research Article

Finite Difference Method for Solving a System of Third-Order Boundary Value Problems

1Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan
2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 2 November 2011; Revised 7 February 2012; Accepted 8 February 2012

Academic Editor: Zhenyu Huang

Copyright © 2012 Muhammad Aslam Noor 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. E. A. Al-Said, “Numerical solutions for system of third-order boundary value problems,” International Journal of Computer Mathematics, vol. 78, no. 1, pp. 111–121, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. E. A. Al-Said and M. A. Noor, “Cubic splines method for a system of third-order boundary value problems,” Applied Mathematics and Computation, vol. 142, no. 2-3, pp. 195–204, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. E. A. Al-Said and M. A. Noor, “Numerical solutions of third-order system of boundary value problems,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 332–338, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. E. A. Al-Said, M. A. Noor, and A. K. Khalifa, “Finite difference scheme for variational inequalities,” Journal of Optimization Theory and Applications, vol. 89, no. 2, pp. 453–459, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. E. A. Al-Said, M. A. Noor, and Th. M. Rassias, “Numerical solutions of third-order obstacle problems,” International Journal of Computer Mathematics, vol. 69, no. 1-2, pp. 75–84, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. S. R. Dunbar, “Geometric analysis of a nonlinear boundary value problem from physical oceanography,” SIAM Journal on Mathematical Analysis, vol. 24, no. 2, pp. 444–465, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. F. Gao and C.-M. Chi, “Solving third-order obstacle problems with quartic B-splines,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 270–274, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 2000.
  9. H. Lewy and G. Stampacchia, “On the regularity of the solution of a variational inequality,” Communications on Pure and Applied Mathematics, vol. 22, pp. 153–188, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. A. Noor, “General variational inequalities,” Applied Mathematics Letters, vol. 1, no. 2, pp. 119–122, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. M. A. Noor, “Variational inequalities in physical oceanography,” in Ocean Waves Engineering, M. Rahman, Ed., pp. 201–266, Computational Mechanics, London, UK, 1994. View at Google Scholar
  12. M. A. Noor, “New approximation schemes for general variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 217–229, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. M. A. Noor, “Some recent advances in variational inequalities. I. Basic concepts,” New Zealand Journal of Mathematics, vol. 26, no. 1, pp. 53–80, 1997. View at Google Scholar · View at Zentralblatt MATH
  14. M. A. Noor, “Some developments in general variational inequalities,” Applied Mathematics and Computation, vol. 152, no. 1, pp. 199–277, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. M. A. Noor, “Extended general variational inequalities,” Applied Mathematics Letters, vol. 22, no. 2, pp. 182–186, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. M. A. Noor and E. A. Al-Said, “Finite-difference method for a system of third-order boundary-value problems,” Journal of Optimization Theory and Applications, vol. 112, no. 3, pp. 627–637, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. A. Noor and E. E. Al-Said, “Quartic splines solutions of third-order obstacle problems,” Applied Mathematics and Computation, vol. 153, no. 2, pp. 307–316, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. M. A. Noor, K. I. Noor, and T. M. Rassias, “Some aspects of variational inequalities,” Journal of Computational and Applied Mathematics, vol. 47, no. 3, pp. 285–312, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. Siraj-ul-Islam, M. A. Khan, I. A. Tirmizi, and E. H. Twizell, “Non polynomial spline approach to the solution of a system of third-order boundary-value problems,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 152–163, 2005. View at Publisher · View at Google Scholar
  20. E. O. Tuck and L. W. Schwartz, “A numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows,” SIAM Review, vol. 32, no. 3, pp. 453–469, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH