Central difference method of a non-standard inverse heat conduction problem for determining surface heat flux from interior observations

In this paper, we consider a non-standard inverse heat conduction problem in a quarter plane. We want to know the surface heat flux from a measured temperature history at a fixed location inside the body. This is a severely ill-posed problem in that arbitrarily “small” differences in the input temperature can result in arbitrarily “large” differences in the surface flux. A central difference schemes in time can restore the stability of “heat flux” solution and error estimate can be obtained. A numerical experiment shows that the method works effectively.