A computational method for an inverse problem in a parabolic system

This note is concerned with the identification of the absorption coefficient in a parabolic system. It introduces an algorithm that can be used to recover the unknown function. The algorithm is iterative in nature. It assumes an initial value for the unknown function and updates it at each iteration. Using the assumed value, the algorithm obtains a background field and computes the equation for the error at each iteration. The error equation includes the correction to the assumed value of the unknown function. Using the measurements obtained at the boundaries, the algorithm introduces two formulations for the error dynamics. By equating the responses of these two formulations it is then possible to obtain an equation for the unknown correction term. A number of numerical examples are also used to study the performance of the algorithm.