title: Stability of operator-difference schemes with weights for the hyperbolic equation in the space of summable functions with carriers in the network-like domain
metadata.name: dc.contributor.author
metadata.value: Zhabko, Aleksei P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Sergeev, Sergey M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-01-19T21:03:34Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-01-19T21:03:34Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zhabko V. P., Provotorov V. V., Sergeev S. M. Stability of operator-difference schemes with weights for the hyperbolic equation in the space of summable functions with carriers in the network-like domain. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2022, vol. 18, iss. 3, pp. 425–437.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.311
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38871
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This work is a natural continuation of the authors’ research on flow phenomena in the direction of increasing the dimensionality of the network-like domain of change of the space variable. The possibility of practical use of the analysis of the stability of operator-difference schemes to solve the issue of stability (stabilization) of wave phenomena in the engineering of the process of transferring continuous media through network-like carriers (water pipelines, gas and oil pipelines, industrial carriers of petroleum products) is shown. Namely, if the scheme is stable, then sufficiently small changes in the initial data of the mathematical model of the process imply small changes of the solution of the difference problem, i. e. in practice do not lead to undesirable aftereffects. If the schema is unstable, then small changes to the initial data can lead to arbitrarily large changes of the solution. In the process of exploitation of industrial constructions of network-like carriers, wave phenomena inevitably arise, the consequence of which are various kinds of instabilities that entail destruction of one nature or another. It is possible to avoid or essentially reduce such undesirable oscillations using the analysis of the stability properties of the mathematical model of the wave process. The obtained results are used in the algorithmically and digitalization of modern technological processes of the movement of fluid media and gases.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 18; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: network-like domain
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: domain adjoining surfaces
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: operator-difference scheme with weights
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability scheme
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stability of operator-difference schemes with weights for the hyperbolic equation in the space of summable functions with carriers in the network-like domain
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 14581-Текст статьи-48034-1-10-20221012.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38871/1/14581-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-48034-1-10-20221012.pdf
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