Numerical solving an inverse problem of source reconstruction for a parabolic equation

In the theory of inverse problems of mathematical physics the problem of reconstructing unknown right hand sides via additional measurements is considered as a basic one. In the present work possibilities of numerical solving this class of problems for parabolic equations are discussed. An unknown dependence of the right hand side on time is reconstructed using the known solution in a particular internal point. The proposed numerical algorithm for approximate solving of the problem is based on a transformation of the initial problem to the boundary value problem for the loaded heat conduction equation. Particular emphasis is on implementation aspects. Test predictions are presented too.