SOLVING OF SECOND ORDER NONLINEAR PDE PROBLEMS BY USING ARTIFICIAL CONTROLS WITH CONTROLLED ERROR

  • Gachpazan, M. (Faculty of Mathematics, Damghan University) ;
  • Kamyad, A.V. (Faculty of Mathematics, Ferdowsi University of Mashhad)
  • Published : 2004.05.01

Abstract

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region in $R^2$. We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error in $L_1$ is controlled.

Keywords

References

  1. Bulletin of the Iranian Mathematical society v.23 no.2 The optimal control of an inhomogeneous wave problem with internal control and their numerical solution S. A. Alavi;A. V. Kamyad;M. H. Farahi
  2. Scientia Iranica v.7 no.1 Solving of nonlinear ordinary differential equations as a control problem by using measure theory S. A. Alavi;A. V. Kamyad;M. Gachpazan
  3. Lectures on Analysis G. Choquet
  4. Journal for analysis and its applications v.19 no.1 On infinite-Horizon optimal control problems, Zeitshrift fur analysis und ihre anwendungen S. Effati;A. V. Kamyad;M. H. Farahi
  5. Ph. D. thesis, Leeds University The boundary control of the wave equation M. H. Farahi
  6. International Journal of Control v.63 The optimal control of the linear wave equation M. H. Farahi;J. E. Rubio;D. A. Wilson
  7. International Journal of Control v.65 no.1 The global control of a nonlinear wave equation M. H. Farahi;J. E. Rubjo;D. A. Wilson
  8. J. Appl. Math. & Computing(old KJCAM) v.7 no.2 A new method for solving nonlinear second order partial differential equations M. Gachpazan;A. Kerayechian;A. V. Kamyad
  9. Bulletin of the Iranian Mathematical society v.18 no.1 Strong controllability of the diffusion equation in n-dimensions A. V. Kamyad
  10. J. Appl. & Math. & Computing Strong controllability and optimal of the heat equation with a thermal source A. V. Kamyad;A. H. Borzabadi
  11. Journal of Optimization Theory and Applications v.75 no.1 An optimal control problem for the multidimensional diffusion equation with a generalized control variable A. V. Kamyad;J. E. Rubio;D. A. Wilson
  12. Journal of Optimization theory and Application v.70 The optimal control of the multidimensional diffusion equation A. V. Kamyad;J. E. Rubio;D. A. Wilson
  13. Basic complex analysis J. E. Marsden;M. J. Hoffman
  14. An introduction to the finite element method J. N. Reddy
  15. Functional analysis and boundary value problems J. L. Reddy
  16. Control and Optimization: The Linear Treatment of nonlinear Problems J. E. Rubio
  17. Numerical solution of partial differential equations: finite defference methods G. D. Smith
  18. Journal of Optimization Theory and Applications v.22 Existence of optimal controls for the diffusion equation D. A. Wilson;J. E. Rubio