In this paper, we will first study the existence and uniqueness of the solution of an inverse problem for a linear equation with nonlinear boundary conditions radiation terms , via an auxiliary problem. Furthermore, a stable numerical algorithm based on the use of the solution to the auxiliary problem as a basis function is proposed. To regularize the resultant illconditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approximation to the solution. Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data.
Inverse problem, Radiation terms, Existence and Uniqueness, Stability, Tikhonov regularization method.
Primary Language  English 

Journal Section  Research Article 
Authors 

Publication Date  December 1, 2012 
Published in Issue  Year 2012, Volume 2, Issue 2 
Bibtex  @ { twmsjaem761711, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {21461147}, eissn = {25871013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2012}, volume = {2}, number = {2}, pages = {195  209}, title = {A NUMERICAL SOLUTION OF AN INVERSE PARABOLIC PROBLEM}, key = {cite}, author = {Pourgholi, Reza and Abtahi, Mortaza and Tabasi, S. Hashem} } 