Geodesic
Extremum principles for the analysis of nonlinear network systems
News of the Kabardin-Balkar scientific center of RAS, no. 2 (2005), pp. 20-28.

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In this article, based on the idea of two interconnected semi-flows in network systems for the transfer of matter or energy, new principles of extremum are proven for the main problem of network analysis. On this basis, the Wood-Charles method of non-Newtonian linearization of the network analysis problem has been refined and generalized. The method differs from existing ones in that it is effective when starting from any point. The presented theorems and method are applicable to nonlinear network systems with lumped parameters, and, in particular, to gas, heat, oil and water supply networks.
Keywords: extremum principle, network systems, Kirchhoff's law, nonlinear network 
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V. Ch. Kudaev. Extremum principles for the analysis of nonlinear network systems. News of the Kabardin-Balkar scientific center of RAS, no. 2 (2005), pp. 20-28. http://geodesic.mathdoc.fr/item/IZKAB_2005_2_a3/

[1] A. P. Merenkov, “Differentsiatsiya metodov rascheta gidravlicheskikh tsepei”, ZhVMiMF, 13:5 (1973)

[2] M. M. Andriyashev, Tekhnika rascheta vodoprovodnoi seti, Sovetskoe zakonodatelstvo, M., 1932

[3] V. G. Lobachev, “Novyi metod uvyazki kolets pri raschete vodoprovodnykh setei”, San. tekhnika, 1934, no. 2

[4] H. Cross, Anakisys of flow in networks of conductors, Eng. Exp. Station of Univ. of Illinois, Urbana, 1936., 29 pp.

[5] M. G. Sukharev, “Ob odnom metode rascheta gazosbornykh setei na vychislitelnykh mashinakh”, Izvestiya vuzov. Neft i gaz, 1965, no. 6, 48–52

[6] D. Martin, G. Peters, “The application of Newtons method of network analysis by digital computer”, J. of the Inst. of water engineers, 17 (1963) | MR | Zbl

[7] V. Ya. Khasilev, K. S. Svetlov, M. K. Takoishvili, “Metod konturnykh raskhodov dlya rascheta gidravlicheskikh tsepei”, Irkutsk, 1968, no. 339-68, SEI SO-VINITI AN SSSR, Moskva

[8] R. Epp, A. Fowler, “Efficient code for steady-state flows in networks”, J. of the Hydraulic division, ASCE, 96:HY1 (1970)

[9] A. G. Evdokimov, “Optimalnye zadachi na inzhenernykh setyakh”, Vischa shkola, 1976

[10] V. Ya. Khasilev, A. P. Merenkov, B. M. Kaganovich, K. S. Svetlov, M. K. Takaishvili, Metody i algoritmy rascheta teplovykh setei, Energiya, M., 1978

[11] Dzh. Maksvell, Traktat ob elektrichestve i magnetizme, Oksford, 1873 | MR

[12] L. D. Shevyakov, “Vyvod formul estestvennogo raspredeleniya vozdukha v gornykh vyrabotkakh iz nachala naimenshei raboty”, Gornyi zhurnal, 1929, no. 1

[13] E. Cherri, U. Millar, “Nekotorye novye ponyatiya i teoremy v oblasti nelineinykh sistem”, V kn.: Avtomaticheskoe regulirovanie, 1954, Izdatelstvo inostrannoi literatury, M.

[14] G. Birkhoff, J. B. Diaz, “Nonlinear network problems”, Quarterly of Applied Math, 13:4 (1956), 431–443 | DOI | MR | Zbl

[15] J. Carteron, “Calcul des veseaux mailes de conduite an laide dune calculatrice electronique”, Grenoble La Houille trice electronique, no. 11, N special A/1956, 173–177, La Houille Blanche, Grenoble

[16] B. N. Pshenichnyi, “Raschet energeticheskikh setei na EVM”, ZhVMiMF, 1962, no. 5

[17] Yu. M. Ermolaev, I. M. Melnik, Ekstremalnye zadachi na grafakh, Naukova dumka, Kiev, 1968 | MR

[18] N. Ts. Koida, Variatsionnye metody gidravlicheskogo rascheta truboprovodov, Vysshaya shkola, Minsk, 1968

[19] E. M. Vasileva, B. Yu. Levit, V. N. Livshits, Nelineinye transportnye zadachi na setyakh, Finansy i statistika, M., 1981 | MR

[20] I. L. Khramovich, Upravlenie vodnymi resursami, Nauchnyi mir, M., 2002

[21] Don J. Wood, O. A. Carl, “Charles Hydraulic network analysis using linear theory”, Journal of the hydraulic division, 98:HY7 (1972)