International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 3, Pages 393-400

Semidiscrete central difference method in time for determining surface temperatures

Zhi Qian, Chu-Li Fu, and Xiang-Tuan Xiong

Department of Mathematics, Lanzhou University, Lanzhou 730000, China

Received 27 May 2004; Revised 20 November 2004

Copyright © 2005 Zhi Qian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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)pE with p>1/2. A numerical example shows that the computational effect of this method is satisfactory.