Identification of the spacewise dependent right-hand side in one-dimensional parabolic equation

Abstract

In this paper we consider numerical solution of the inverse problem of determining a spacewise dependent right-hand side function, which is also called source function, in parabolic equation from measured data of the solution at the final time point. Such inverse problem occurs in mathematical modeling of various physics or engineering areas. Special iterative method is constructed for the approximate solution of the inverse problem, based on the source function at the new iterative step can be identified by the time derivative and space derivative at final time moment. The capabilities of the proposed computational algorithm is confirmed by the results of several numerical experiments.