Abstract:
In the paper, the stability conditions of a three-layer symmetric differential-difference scheme with a weight parameter in the class of functions summable on a network-like domain are obtained.
To analyze the stability of the differential-difference system in the space of feasible solutions H, a composite norm is introduced that has the structure of a norm in the space H2=H⊕H.
Namely, for Y={Y1,Y2}∈H2,Yℓ∈H (ℓ=1,2), ‖Y‖2H=‖Y1‖21,H+‖Y2‖22,H, where ‖⋅‖21,H‖⋅‖22,H are some norms in H.
The use of such a norm in the description of the energy identity opens the way for constructing a priori estimates for weak solutions of the differential-difference system, convenient for practical testing in the case of specific differential-difference schemes.
The results obtained can be used to analyze optimization problems that arise when modeling network-like transfer processes with the help of formalisms of differential-difference systems.
Keywords:
multidimensional network-like domain, differential-difference system, stability of differential-difference scheme.
Citation:
V. V. Provotorov, V. N. Hoang, “Stability of a three-layer symmetric differential-difference scheme in the class of functions summable on a network-like domain”, Russian Universities Reports. Mathematics, 27:137 (2022), 80–94
\Bibitem{ProHoa22}
\by V.~V.~Provotorov, V.~N.~Hoang
\paper Stability of a three-layer symmetric differential-difference scheme in the class of functions summable on a network-like domain
\jour Russian Universities Reports. Mathematics
\yr 2022
\vol 27
\issue 137
\pages 80--94
\mathnet{http://mi.mathnet.ru/vtamu248}
\crossref{https://doi.org/10.20310/2686-9667-2022-27-137-80-94}
Linking options:
https://www.mathnet.ru/eng/vtamu248
https://www.mathnet.ru/eng/vtamu/v27/i137/p80
This publication is cited in the following 3 articles:
M. B. Zvereva, M. I. Kamenskii, “Problem on string system vibrations on star-shaped graph with nonlinear condition at node”, Ufa Math. J., 16:1 (2024), 34–52
V. N. Khoang, V. V. Provotorov, “Ustoichivost trekhsloinykh differentsialno-raznostnykh skhem s vesami v prostranstve summiruemykh funktsii s nositelyami v setepodobnoi oblasti”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 23:3 (2023), 357–369
M. B. Zvereva, “A model of string system deformations on a star graph with nonlinear condition at the node”, CMFD, 68:4 (2022), 635–652