Semidiscrete central difference method in time for determining surface temperatures

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 onthe 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