The fully-implicit finite difference method for solving nonlinear inverse parabolic problems with unknown source term

Autor:	Reza Pourgholi, Sahar Tavana, Hassan Dana Mazraeh
Rok vydání:	2018
Předmět:	Applied Mathematics Finite difference method Inverse Inverse problem Theoretical Computer Science Tikhonov regularization Computational Mathematics Nonlinear system Unknown Source Computational Theory and Mathematics Numerical approximation Applied mathematics Heat equation Mathematics
Zdroj:	International Journal of Computing Science and Mathematics. 9:405
ISSN:	1752-5063 1752-5055
DOI:	10.1504/ijcsm.2018.10015907
Popis:	A numerical procedure based on a fully implicit finite difference method for an inverse problem of identification of an unknown source in a heat equation is presented. The approach of the proposed method is to approximate unknown function from the solution of the minimisation problem based on the overspecified data. This problem is ill-posed, in the sense that the solution (if it exist) does not depend continuously on the data. To regularise this ill-conditioned, we apply the Tikhonov regularisation 0th, 1st and 2nd method to obtain the stable numerical approximation to the solution. A stability analysis shows that this numerical scheme approximation is unconditionally stable. Numerical results for two inverse source identification problems show that the proposed numerical algorithm is simple, accurate, stable and computationally efficient.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e0b875b3eb2aff59ce44a7b8fc717cf https://doi.org/10.1504/ijcsm.2018.10015907 Zobrazit plný text záznamu