A numerical approach for solving a nonlinear inverse diusion problem by Tikhonov regularization

Subject Areas : Applied Mathematics

H. Molhem ¹ , R. Pourgholi ² , M. Borghei ³

1 - Department of Physics , Faculty of Science, Islamic Azad University, Karaj Branch, Karaj, Iran
2 - School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran.
3 - Department of Physics , Faculty of Science, Islamic Azad University, Karaj Branch, Karaj, Iran.

Received: 2015-09-28 Accepted : 2015-09-28 Published : 2013-12-01

Keywords: Laplace transform, Inverse nonlinear diusion problem, Finite dierence method, Least-squares method, Regularization method, SVD Method,

Abstract :

In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted tond the solution. To regularize the resultant ill-conditioned linear system ofequations, we apply the Tikhonov regularization method to obtain the stablenumerical approximation to the solution. Some numerical experiments con-rm the utility of this algorithm as the results are in good agreement with theexact data.

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