title: Monte Carlo method for solution of systems ODE
metadata.name: dc.contributor.author
metadata.value: Ermakov, Sergey M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tovstik, Tatiana M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-09-05T16:17:15Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-09-05T16:17:15Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ermakov S.M., Tovstik T.M. Monte Carlo method for solution of systems ODE. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 3, pp. 411–421.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.306
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16317
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: An application of the Monte Carlo method to solution of problems Cauchy for system of linear and nonlinear ordinary differential equations is considered. the Monte Carlo method is topical for solution of large systems of equations and in the cases with given functions are not smooth enough. A system is reduced to an equivalent system of integral equations of the Volterra type. For linear systems this transformation allows to avoid restrictions, connected with a convergence of a majorizing process. Examples of estimates of functionals of solutions are given, and a behavior of their dispersions are discussed. In the general case an interval of solution is divided into finite subintervals in that nonlinear functions are approximated by polynomials. An obtained integral equations are solved by using branching Markov chains with an absorption. Appearing problems of parallel algorithms are discussed. As an example an one dimensional cubic equation is considered. A method of levels of branching process is discussed in details. a comparison of numerical results with a solution, obtained by the Runge Kutta method, is presented.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Russian Foundation for Basic Research (grand N17-01-00267-а).
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 6 (64); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: Monte Carlo method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: systems ODE
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: statistic simulation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Monte Carlo method for solution of systems ODE
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 411-421.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16317/1/411-421.pdf
resources.format: Adobe PDF
resources.size: 318,19 kB