Numerical solution of forward and backward problem for 2-D heat conduction equation

Authors:
Jijun Liu
Affiliations:
Department of Applied Mathematics, Southeast University, Nanjing 210096, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

For a two-dimensional heat conduction problem, we consider its initial boundary value problem and the related inverse problem of determining the initial temperature distribution from transient temperature measurements. The conditional stability for this inverse problem and the error analysis for the Tikhonov regularization are presented. An implicit inversion method, which is based on the regularization technique and the successive over-relaxation (SOR) iteration process, is established. Due to the explicit difference scheme for a direct heat problem developed in this paper, the inversion process is very efficient, while the application of SOR technique makes our inversion convergent rapidly. Numerical results illustrating our method are also given.