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.‎ تفاصيل المقالة