Reconstructing an unknown time-dependent function in the boundary conditions of a parabolic PDE

This work investigates the parabolic inverse problem of reconstructing an unknown time-dependent function in the boundary conditions from additional terminal, integral or point observations. A numerical scheme is developed for obtaining an approximate solution for this problem. The method consists of reducing the solution of the inverse problem to a system of integral equations. The properties of Sinc function are then utilized for replacing the resulting integral equations by a system of linear algebraic equations. Several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method.