title: Application of the implicit Euler method for the discretization of some classes of nonlinear systems
metadata.name: dc.contributor.author
metadata.value: Aleksandrov, Alexander Yu.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-10-23T17:51:13Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-10-23T17:51:13Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Aleksandrov A. Yu. Application of the implicit Euler method for the discretization of some classes of nonlinear systems. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2023, vol. 19, iss. 3, pp. 304–319. https://doi.org/10.21638/11701/spbu10.2023.301 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2023.301
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44286
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of stability preservation under discretization of some classes of nonlinear differential
  equations systems is studied. Persidskii systems, Lurie systems of indirect control, and systems whose right-hand sides have a canonical structure are considered. It is assumed
  that the zero solutions of these systems are globally asymptotically stable. Conditions are determined
  that guarantee the asymptotic stability of the zero solutions for the corresponding
  difference systems. Previously, such conditions were established for the case where discretization
  was carried out using the explicit Euler method. In this paper, difference schemes are
  constructed on the basis of the implicit Euler method. For the obtained discrete systems,
  theorems on local and global asymptotic stability are proved, estimates of the time of transient
  processes are derived. For systems with a canonical structure of right-hand sides, based
  on the approach of V. I. Zubov, a modified implicit computational scheme is proposed that
  ensures the matching of the convergence rate of solutions to the origin for the differential
  and corresponding difference systems. It is shown that implicit computational schemes can
  guarantee the preservation of asymptotic stability under less stringent constraints on the
  discretization step and right-hand sides of the systems under consideration compared to the
  constraints obtained using the explicit method. An example is presented illustrating the obtained
  theoretical conclusions.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
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 19; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: difference systems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: discretization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: implicit Euler method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov functions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: conservative numerical methods
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Application of the implicit Euler method for the discretization of some classes of nonlinear systems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44286/1/01.pdf
resources.format: Adobe PDF
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