The method of central difference for the inverse time-dependent heat source problem

This paper investigates the inverse problem of determining a heat source in a parabolic equation where data are given at some fixed location. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. A central difference regularization method is given and an order optimal stability estimate is obtained. Numerical results for several benchmark test problems indicate that the central difference regularization method is an accurate and flexible method to determine the unknown time-dependent heat source.