Skip to main content
Log in

Finite difference scheme for variational inequalities

  • Technical Note
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, we show that a class of variational inequalities related with odd-order obstacle problems can be characterized by a system of differential equations, which are solved using the finite difference scheme. The variational inequality formulation is used to discuss the uniqueness and existence of the solution of the obstacle problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Stampacchia, G.,Formes Bilineaires Coercitives sur les Ensembles Convexes, Comptes Rendus de l'Academie des Sciences, Paris, Vol. 258, pp. 4413–4416, 1964.

    Google Scholar 

  2. Noor, M. A., Noor, K. I., andRassias, T. M.,Some Aspects of Variational Inequalities, Journal of Computational and Applied Mathematics, Vol. 47, pp. 285–312, 1993.

    Google Scholar 

  3. Kinderlehrer, D., andStampacchia, G.,An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, New York, 1980.

    Google Scholar 

  4. Cottle, R. W., Giannessi, F., andLions, J. L.,Variational Inequalities and Complementarity Problems, J. Wiley and Sons, New York, New York, 1980.

    Google Scholar 

  5. Glowinski, R., Lions, J. L., andTremolieres, R.,Numerical Analysis of Variational Inequalities, North Holland, Amsterdam, Holland, 1981.

    Google Scholar 

  6. Al-Gwaiz, M. A.,Theory of Distributions, Marcel Dekker, New York, New York, 1992.

    Google Scholar 

  7. Kikuchi, N., andOden, J. T.,Contact Problems in Elasticity, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1988.

    Google Scholar 

  8. Noor, M. A.,Wiener-Hopf Equations and Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 79, pp. 197–206, 1994.

    Google Scholar 

  9. Noor, M. A.,Variational Inequalities in Physical Oceanography, Ocean Waves Engineering, Edited by M. Rahman, Computational Mechanics Publications, Southampton, England, pp. 201–226, 1994.

    Google Scholar 

  10. Lewy, H., andStampacchia, G.,On the Regularity of the Solutions of the Variational Inequalities, Communication on Pure and Applied Mathematics, Vol. 22, pp. 153–188, 1969.

    Google Scholar 

  11. Noor, M. A., andKhalifa, A. K.,Quintic Splines for Solving Contact Problems, Applied Mathematics Letters, Vol. 3, pp. 81–83, 1990.

    Google Scholar 

  12. Noor, M. A., andKhalifa, A. K.,Cubic Splines Collocation Methods for Unilateral Problems, International Journal of Engineering Science, Vol. 25, pp. 1525–1530, 1987.

    Google Scholar 

  13. Noor, M. A., andKhalifa, A. K.,A Numerical Approach for Odd Order Obstacle Problems, International Journal of Computer Mathematics, Vol. 54, pp. 109–116, 1994.

    Google Scholar 

  14. Dunbar, S. R.,Geometric Analysis of Nonlinear Boundary-Value Problems from Physical Oceanography, SIAM Journal on Mathematical Analysis, Vol. 24, pp. 444–465, 1993.

    Google Scholar 

  15. Noor, M. A.,General Variational Inequalities, Applied Mathematics Letters, Vol. 1, pp. 119–122, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by F. Giannessi

Rights and permissions

Reprints and permissions

About this article

Cite this article

Al-Said, E.A., Noor, M.A. & Khalifa, A.K. Finite difference scheme for variational inequalities. J Optim Theory Appl 89, 453–459 (1996). https://doi.org/10.1007/BF02192538

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02192538

Key Words

Navigation