A numerical method based on Sinc functions for solving an inverse time-dependent source term problem

In this paper, an inverse problem of determining an unknown time-dependent source term in a parabolic equation is considered. A numerical algorithm based on Sinc function is presented for recovering the unknown function and obtaining a solution of the problem. For solving the problem, a Galerkin method with the Sinc basis functions in both the space and time domains combined with the Tikhonov regularization is presented to obtain a stable solution. The approximate solution displays an exponential convergence rate.