A computational method for identifying a spacewise‐dependent heat source

In this paper, we consider a finite difference approximation to an inverse problem of determining a spacewise‐dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time. Since the resulting matrix equation is ill‐conditioned, a regularized solution is obtained by employing the truncated singular value decomposition to solve the matrix equation arising from the finite difference method, with the optimal regularization parameter determined by the generalized cross‐validation criterion. The effectiveness of the proposed numerical scheme is illustrated by several continuous and discontinuous numerical examples.