Resolution of an inverse parabolic problem using Sinc-Galerkin method

In this paper, a numerical method is proposed to solve an Inverse Heat Conduction Problem (IHCP) using noisy data based on Sinc-Galerkin method. A stable numerical solution is determined for the problem. To do this, we use a sensor located at a point inside the body and measure u(x; t) at a point x = a, where 0 < a < 1. We also show that the rate of convergence of the method is as exponential. The numerical results show the efficiency of our approach to estimate the unknown functions of the inverse problem. The function can be computed within a couple of minutes CPU time at pentium IV-2.7 GHz PC.