document: Numerical solution of forward and backward problem for 2-D heat conduction equation 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 -LRB- SOR -RRB- 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
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