The proposed work is a continuation of research aimed at developing algorithms embedded in the servers of integrated platforms for the functioning
of logistics network processes, and in demand in the tasks of forming a stable digital environment. Based on the principles laid down in the concept of
Industry 4.0, all modern software solutions are built on the basis of complex mathematical models that play the role of digital twins. Only in this way is the
main goal achieved — the search for an optimal management solution. The logistics tasks currently under consideration, as a rule, were formulated only
as one-dimensional supply chains or simple tasks of forming consumer value on mathematical graphs, in the form of which the image of network logistics
and commercial structures is presented. The trend towards digitalization and the introduction of artificial intelligence systems at the stage of managerial
decision-making, which is necessary for sustainable work in a competitive environment, dictates the need to create algorithms and models that much more
adequately reflect the essence of real processes and are as relevant as possible both in economic and technological aspects. The results of this study allow
us to take into account an additional important factor of the multidimensionality of the displacement processes. This circumstance is always present when
moving continuous flows between nodes of the logistics network, and is also, as a rule, characteristic of discrete flows.
Keywords: digitalization, network-like n-dimensional domain, logistics, initial boundary value problem, semi-discretization method, algorithm
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