implementation of sinc-galerkin on parabolic inverse problem with unknown boundary ‎condition‎

The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. for solving these ill-posed inverse problems, galerkin method based on sinc basis functions for space and time will be used. to solve the system of linear equation, a noise is imposed and tikhonove regularization is applied. by using a sensor located at a point in the domain of $x$, say $x=a'$, and determining $u(a',t)$ a stable solution will be achived. an illustrative example is provided to show the ability and the efficiency of this numerical ‎approach.‎