Data Recovering Problem Using a New KMF Algorithm for Annular Domain

Autor:	Otman Abdoun, Chakir Tajani, Jaafar Abouchabaka
Rok vydání:	2012
Předmět:	Laplace's equation Unit circle Laplace transform Iterative method Boundary (topology) Initial value problem General Medicine Inverse problem Algorithm Mathematics Domain (software engineering)
Zdroj:	American Journal of Computational Mathematics. :88-94
ISSN:	2161-1211 2161-1203
DOI:	10.4236/ajcm.2012.22012
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1b218f2d7b3adf6e57a096e1929aea5c https://doi.org/10.4236/ajcm.2012.22012 Zobrazit plný text záznamu