Implementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary ‎condition‎

Subject Areas : International Journal of Industrial Mathematics

J. Biazar ¹ , T. Houlari ²

1 - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-1914, Guilan, Rasht, Iran.
2 - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-1914, Guilan, Rasht, Iran.

Received: 2015-10-01 Accepted : 2015-10-01 Published : 2015-10-01

Keywords: Ill-posed inverse problems, Sinc-Galerkin method, Tikhonov regularization, ‎U‎nkown boundary ‎condition,

Abstract :

The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $x=a'$, and determining $u(a',t)$ a stable solution will be achived. An illustrative example is provided to show the ability and the efficiency of this numerical ‎approach.‎