Stability of a three-layer symmetric differential-difference scheme in the class of functions summable on a network-like domain
Vestnik rossijskih universitetov. Matematika, Tome 27 (2022) no. 137, pp. 80-94
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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 $H^2=H\oplus H.$
Namely, for $Y=\{Y_1,Y_2\}\in H^2,$ $Y_\ell\in H$ ($\ell=1,2$), $\| Y\|^2_H=\| Y_1\|^2_{1,H}+\| Y_2\|^2_{2,H},$ where $\|\cdot\|^2_{1,H}$ $\|\cdot\|^2_{2,H}$ 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.
@article{VTAMU_2022_27_137_a5,
author = {V. V. Provotorov and V. N. Hoang},
title = {Stability of a three-layer symmetric differential-difference scheme in the class of functions summable on a network-like domain},
journal = {Vestnik rossijskih universitetov. Matematika},
pages = {80--94},
publisher = {mathdoc},
volume = {27},
number = {137},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTAMU_2022_27_137_a5/}
}
TY - JOUR AU - V. V. Provotorov AU - V. N. Hoang TI - Stability of a three-layer symmetric differential-difference scheme in the class of functions summable on a network-like domain JO - Vestnik rossijskih universitetov. Matematika PY - 2022 SP - 80 EP - 94 VL - 27 IS - 137 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VTAMU_2022_27_137_a5/ LA - ru ID - VTAMU_2022_27_137_a5 ER -
%0 Journal Article %A V. V. Provotorov %A V. N. Hoang %T Stability of a three-layer symmetric differential-difference scheme in the class of functions summable on a network-like domain %J Vestnik rossijskih universitetov. Matematika %D 2022 %P 80-94 %V 27 %N 137 %I mathdoc %U http://geodesic.mathdoc.fr/item/VTAMU_2022_27_137_a5/ %G ru %F VTAMU_2022_27_137_a5
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. Vestnik rossijskih universitetov. Matematika, Tome 27 (2022) no. 137, pp. 80-94. http://geodesic.mathdoc.fr/item/VTAMU_2022_27_137_a5/