Current Mechanical Engineering Production has a complicated network structure for technological processes providing. Equipment digitization of material transition allows you to get a real-time slice of economically important indicators. Also, the whole dynamics of production functionality can be presented in the formal view by mathematical models. The article deals with transference processes in linear commercial networks, which are network-like diffusive phenomena described by classical equations of mathematical physics. In addition, many problems of mathematical physics lead to the necessity to define coefficients in the partial differential equation and coefficients in boundary conditions with known functionals from the solution of the matching initial - boundary value problem. In case of depending coefficients in the differential equation on a spatial variable, the real presentation of the solution makes it impossible to define these coefficients. Therefore, other approaches, in particular, spectral ones figure in this article.

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