A NEW METHOD FOR SOLVING NONLINEAR SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS

  • Gachpazan. M. (Dept. of Mathematics, Ferdowsi University of Mashhad) ;
  • Kerayechian, A. (Dept. of Mathematics, Ferdowsi University of Mashhad) ;
  • Kamyad, A.V. (Dept. of Mathematics, Ferdowsi University of Mashhad)
  • Published : 2000.05.01

Abstract

In this paper, a new method for finding the approximate solution of a second order nonlinear partial differential equation is introduced. In this method the problem is transformed to an equivalent optimization problem. them , by considering it as a distributed parameter control system the theory of measure is used for obtaining the approximate solution of the original problem.

Keywords

References

  1. Solving of nonlinear ordinary differential equations as a control problem by using measure theory, to appear. S. A. Alavi;A. V. Kamyad;M. Gachpazan
  2. 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
  3. Lectures on Analysis G. Choquet
  4. Int. J. of Control v.63 no.1 The optimal control of the linear wave equation M. H. Farahi;J. E. Rubio;D. A. Wilson
  5. Int. of Control v.65 no.1 The global control of a nonlinear wave equation M. H. Farahi;J. E. Rubio;D. A. Wilson
  6. Ph.D. thesis The boundary control of the wave equation M. H. Farahi
  7. J. of Optimization theory and Application v.70 The optimal control of the multidimensional diffusion equation A. V. Kamyad;J. E. Rubio;D. A. Wilson
  8. J. 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
  9. Bulletin of the Iranian Mathematical society v.18 no.1 Strong controllability of the diffusion equation in n-dimensions A. V. Kamyad
  10. Functional analysis and boundary value problems J. L. Reddy
  11. An introduction to the finite element method J. N .Reddy
  12. Manchester Control and Optimization: The Linear Treatment of nonlinear Problems J. E. Rubio
  13. Numerical solution of partial differential equations: finite defference methods G. D. Smith
  14. J. of Optimization Theory and Applications v.22 Existence of optimal controls for the diffusion equation D. A. Wilson;J. E. Rubio