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

*(English)*Zbl 1005.65107The 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.

Reviewer: Zhang Whanguo (Shanghai)

##### 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 |

##### Keywords:

heat equation; difference scheme; inverse problem; successive overrelaxation; Tikhonov regularization; numerical examples; stability; error analysis
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\textit{J. Liu}, J. Comput. Appl. Math. 145, No. 2, 459--482 (2002; Zbl 1005.65107)

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##### References:

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