Introduce of the auxiliary function for calculation and development of algorithms for functioning and management of main gas pipelines

The relevance of the work is due to the need to find ways to improve work efficiency, as well as improving the mathematical and software procedures for the optimal development of pipeline networks, therefore, this article focuses on the analysis of mathematical models and the creation of computational algorithms for the operation and management of singleline and interconnected multi-line gas pipelines in dynamic gas transport mode, allowing to cover the processes occurring in pipeline systems in various situations. A generalized methodology has been developed for the operational control of the operating modes of single-line MGs with concentrated gas extraction and pumping, with variable diameters for a dynamic gas consumption regime for various tasks of boundary conditions at the CS input and output. A new function has been introduced that smooths flow discontinuities in elementary sections and during the transition from one diameter (or section) to another.