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Semidiscrete central difference method in time for determining surface temperatures

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  • Zhi Qian
  • Chu-Li Fu
  • Xiang-Tuan Xiong

Abstract

We consider an inverse heat conduction problem (IHCP) in a quarter plane. We want to know the distribution of surface temperature in a body from a measured temperature history at a fixed location inside the body. This is a severely ill-posed problem in the sense that the solution (if exists) does not depend continuously on the data. Eldén (1995) has used a difference method for solving this problem, but he did not obtain the convergence at x = 0 . In this paper, we gave a logarithmic stability of the approximation solution at x = 0 under a stronger a priori assumption ‖ u ( 0 , t ) ‖ p ≤ E with p > 1 / 2 . A numerical example shows that the computational effect of this method is satisfactory.

Suggested Citation

  • Zhi Qian & Chu-Li Fu & Xiang-Tuan Xiong, 2005. "Semidiscrete central difference method in time for determining surface temperatures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:862939
    DOI: 10.1155/IJMMS.2005.393
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