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Numerical solution of forward and backward problem for 2-D heat conduction equation. (English) Zbl 1005.65107
The author discusses the two-dimensional inverse heat conduction problem, which determines 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 overrelaxation iteration process, is established. This paper also develops an explicit difference scheme for a direct efficient, while the application of the successive over-relaxation technique makes this inversion convergent rapidly. Lastly some numerical examples are given.

MSC:
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R30 Inverse problems for PDEs
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