title: Monte-Carlo for solving large linear systems of ordinary differential equations
metadata.name: dc.contributor.author
metadata.value: Ermakov, Sergey M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Smilovitskiy, Maxim G.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-05-04T18:56:50Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-05-04T18:56:50Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ermakov S.M., Smilovitskiy M.G. Monte-Carlo for solving large linear systems of ordinary differential equations. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 1, pp. 37–48.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.104
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/28432
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Monte-Carlo approach towards solving Cauchy problem for large systems of linear differential
  equations is being proposed in this paper. Firstly, a quick overlook of previously
  obtained results from applying the approach towards Fredholm-type integral equations is
  being made. In the main part of the paper, a similar method is being applied towards a
  linear system of ODE. It is transformed into an equivalent system of Volterra-type integral
  equations, which relaxes certain limitations being present due to necessary conditions for
  convergence of majorant series. The following theorems are being stated. Theorem 1 provides
  necessary compliance conditions that need to be imposed upon initial and transition
  distributions of a required Markov chain, for which an equality between estimate’s expectation
  and a desirable vector product would hold. Theorem 2 formulates an equation that
  governs estimate’s variance, while theorem 3 states a form for Markov chain parameters that
  minimise the variance. Proofs are given, following the statements. A system of linear ODEs
  that describe a closed queue made up of ten virtual machines and seven virtual service
  hubs is then solved using the proposed approach. Solutions are being obtained both for a
  system with constant coefficients and time-variable coefficients, where breakdown intensity
  is dependent on t. Comparison is being made between Monte-Carlo and Rungge Kutta  
  obtained solutions. The results can be found in corresponding tables.
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. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: Monte-Carlo
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: ODE system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: queuing theory
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal density
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: unbiased estimate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: statistical modelling
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Monte-Carlo for solving large linear systems of ordinary differential equations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 37-48.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/28432/1/37-48.pdf
resources.format: Adobe PDF
resources.size: 323,53 kB