Analysis of approaches to mass-transfer modeling n non-stationary mode: Fìz.-mat. model. ìnf. tehnol. 2020, 28:55-64 - Pyanylo, Yaroslav; Pyanylo, Galyna (PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, 2020)
A significant number of natural and physical processes are described by differential equations in partial derivatives or systems of differential equations in partial derivatives. Numerical methods have been found to find their solutions. Partial derivatives systems are solved mainly by reducing the order of the system of equations or reducing it to one differential equation. This procedure leads to an increase in the order of the differential equation. There are various restrictions and errors that can lead to additional solutions, boundary conditions for intermediate derivatives, and so on. The work is devoted to the analysis of such situations and ways of exit. References Pyanylo, Ya. D., Prytula, M. G. , Prytula, N. M. , Lopuh, N. B. (2014). Models of mass transfer in gas transmission systems. Mathematical modeling and computing, 1(1), 84-96. Pyanylo, Ya. D., Gladun, S. V. (2015). Оptimization of energy costs for gas transportation in complex gas transmission systems. ANNALS of Faculty Engineering Hunedoara — International Journal of Engineering 31. Bobrovskij, S. A., Sherbakov, S. G., Yakovlev, E. I. (1976). Truboprovodnyj transport gaza. M.: Nauka. Bilushchak, Yu., Haivas, B., Hera, B., & Chaplia, Ye. (Eds.). (2019). Matematychne modeliuvannia nerivnovazhnykh protsesiv u skladnykh systemakh. Lviv: NAN Ukrainy, Rastr-7. Pianylo, Ya., Pianylo, H. (2009). Doslidzhennia vplyvu teplofizychnykh parametriv na protses rukhu hazu v truboprovodakh. Fizyko — matematychne modeliuvannia ta informatsiini tekhnolohii, 10, 58-69. Pianylo, Ya. D. (2011). Proektsiino-iteratsiini metody rozviazuvannia priamykh ta obernenykh zadach perenosu. Lviv: Splain. Prytula, N. (2012). Matematychne modeliuvannia perekhidnykh protsesiv v systemakh transportuvannia hazu. Visnyk Natsionalnoho universytetu "Lvivska politekhnika". Kompiuterni nauky ta informatsiini tekhnolohii, 744, 169-172. Sardanashvili, S. A. (2005). Raschetnye metody i algoritmy.M.: Izd — vo “Neft i gaz”. Charnyj, I. A. (1975). Neustanovivsheesya dvizhenie realnoj zhidkosti v trubah. M.: Nedra.