Electron. J. Diff. Equ., Vol. 2015 (2015), No. 188, pp. 1-15.

Numerical solution to inverse elliptic problem with Neumann type overdetermination and mixed boundary conditions

Charyyar Ashyralyyev, Yasar Akkan

Abstract:
This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.

Submitted June 23, 2015. Published July 13, 2015.
Math Subject Classifications: 35N25, 39A14, 39A30, 65J22.
Key Words: Inverse elliptic problem; stability; almost coercive stability; overdetermination; difference scheme.

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Charyyar Ashyralyyev
Department of Mathematical Engineering
Gumushane University, Gumushane, Turkey
email: charyyar@gumushane.edu.tr
Yasar Akkan
Department of Mathematical Engineering
Gumushane University, Gumushane, Turkey
email: akkanyasar61@gumushane.edu.tr

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