Geodesic
On discrete systems with potential operators
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 3, pp. 74-82

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The main purpose of this work is to study the potentiality of a discrete system obtained from the system of the form $C(t, u)\dot u (t) + E(t, u) = 0$ with continuous time. The definition of potentiality of the corresponding discrete system is introduced. Necessary and sufficient conditions for its potentiality with respect to a given bilinear form are obtained. The algorithm for the construction of the corresponding functional—the analogue of the Hamiltonian action—is presented. The illustrative example is given.
Keywords: potential operators, discrete systems. 
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     title = {On discrete systems with potential operators},
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V. M. Savchin; P. T. Trinh. On discrete systems with potential operators. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 3, pp. 74-82. http://geodesic.mathdoc.fr/item/VSGU_2021_27_3_a5/