Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на этот ресурс:
http://hdl.handle.net/11701/28432
Полная запись метаданных
Поле DC | Значение | Язык |
---|---|---|
dc.contributor.author | Ermakov, Sergey M. | - |
dc.contributor.author | Smilovitskiy, Maxim G. | - |
dc.date.accessioned | 2021-05-04T18:56:50Z | - |
dc.date.available | 2021-05-04T18:56:50Z | - |
dc.date.issued | 2021-03 | - |
dc.identifier.citation | 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. | en_GB |
dc.identifier.other | https://doi.org/10.21638/spbu01.2021.104 | - |
dc.identifier.uri | http://hdl.handle.net/11701/28432 | - |
dc.description.abstract | 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. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 1 | - |
dc.subject | Monte-Carlo | en_GB |
dc.subject | ODE system | en_GB |
dc.subject | integral equation | en_GB |
dc.subject | queuing theory | en_GB |
dc.subject | optimal density | en_GB |
dc.subject | unbiased estimate | en_GB |
dc.subject | statistical modelling | en_GB |
dc.title | Monte-Carlo for solving large linear systems of ordinary differential equations | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 1 |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
---|---|---|---|---|
37-48.pdf | 323,53 kB | Adobe PDF | Просмотреть/Открыть |
Все ресурсы в архиве электронных ресурсов защищены авторским правом, все права сохранены.