Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

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

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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

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