AJCM  Vol.2 No.2 , June 2012
Data Recovering Problem Using a New KMF Algorithm for Annular Domain
Abstract: This paper is interested at the Cauchy problem for Laplace’s equation, which is to recover both Dirichlet and Neumann conditions on the inaccessible part of the boundary (inner part) of an annular domain from the over specified conditions on the accessible one (outer part). This work is an extension of the proposed algorithm for a unit circle [1] to annular domain, where, we describe an alternating formulation of the KMF algorithm proposed by Kozlov, Mazya and Fomin, and its relationship with the standard formulation. The new KMF algorithm ameliorates the accuracy of the solution and reduces the number of iterations required to achieve convergence. In the last part, the discussion of the error estimation of solution is presented and some numerical tests, using the software Freefem are given to show the efficiency of the proposed method.
Cite this paper: C. Tajani, J. Abouchabaka and O. Abdoun, "Data Recovering Problem Using a New KMF Algorithm for Annular Domain," American Journal of Computational Mathematics, Vol. 2 No. 2, 2012, pp. 88-94. doi: 10.4236/ajcm.2012.22012.

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