R. Pourgholi, F. Torabi, S. H. Tabasi
Journal of Advanced Research in Scientific Computing, - 3, 3, 55-68 - July, 2011 - .
Publication year: 2011

Abstract

In this paper, the ADI scheme is used to solve the two-dimensional inverse heat conduction problem (IHCP). To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization 0th, 1st and 2nd method to obtain the stable numerical approximation to the solution. It is shown that the regularized solution is dependent continuously upon the data and is an approximation of the exact solution of the two-dimensional IHCP. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method. In reality, this study considers a comparative study between Tikhonov regularization and SVD methods. Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data.