The solution of the diffusion equation at the non-stationary boundary represents the so-called Stefan problem which can be solved by means of the thermal potential of a double-layer with the accuracy sufficient for description of diffusion phenomena. The results were methods for determination of the mean values of the interdiffusion coefficients. The interface boundary shift and diffusivity in the diffusion joints can be determined very precisely from the areas below and above the concentration curve. The diffusivities in the Ni/Ni-Al and Fe/Fe-Mn diffusion joints were calculated from the experimental data using the balance equations that express the law of conservation of the diffusing material in the specimens and on the interface boundary. A new computer program (in Matlab) for the simulation of diffusion processes has been developed.