Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111188
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dc.contributor.authorMilstein, G. N.en
dc.contributor.authorRepin, Yu. M.en
dc.contributor.authorTretyakov, M. V.en
dc.date.accessioned2022-05-12T08:14:08Z-
dc.date.available2022-05-12T08:14:08Z-
dc.date.issued2002-
dc.identifier.citationMilstein G. N. Numerical Methods for Stochastic Systems Preserving Symplectic Structure / G. N. Milstein, Yu. M. Repin, M. V. Tretyakov // SIAM Journal on Numerical Analysis. — 2002. — Vol. 40. — Iss. 4. — P. 1583-1604.en
dc.identifier.issn0036-1429-
dc.identifier.otherAll Open Access, Green3
dc.identifier.urihttp://hdl.handle.net/10995/111188-
dc.description.abstractStochastic Hamiltonian systems with multiplicative noise, phase flows of which preserve symplectic structure, are considered. To construct symplectic methods for such systems, sufficiently general fully implicit schemes, i.e., schemes with implicitness both in deterministic and stochastic terms, are needed. A new class of fully implicit methods for stochastic systems is proposed. Increments of Wiener processes in these fully implicit schemes are substituted by some truncated random variables. A number of symplectic integrators is constructed. Special attention is paid to systems with separable Hamiltonians. Some results of numerical experiments are presented. They demonstrate superiority of the proposed symplectic methods over very long times in comparison with nonsymplectic ones.en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceSIAM J Numer Anal2
dc.sourceSIAM Journal on Numerical Analysisen
dc.subjectIMPLICIT METHODSen
dc.subjectMEAN-SQUARE CONVERGENCEen
dc.subjectSTOCHASTIC HAMILTONIAN SYSTEMSen
dc.subjectSYMPLECTIC INTEGRATIONen
dc.subjectCONVERGENCE OF NUMERICAL METHODSen
dc.subjectDIFFERENTIAL EQUATIONSen
dc.subjectFINITE ELEMENT METHODen
dc.subjectHAMILTONIANSen
dc.subjectMEAN-SQUARE CONVERGENCEen
dc.subjectRANDOM PROCESSESen
dc.titleNumerical Methods for Stochastic Systems Preserving Symplectic Structureen
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/submittedVersionen
dc.identifier.scopus0141869053-
local.contributor.employeeMilstein, G.N., Weierstra-Inst. Angew. Anal./S., Mohrenstr. 39, D-10117 Berlin, Germany, Department of Mathematics, Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russian Federation; Repin, Yu.M., Department of Mathematics, Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russian Federation; Tretyakov, M.V., Department of Mathematics, University of Wales Swansea, Swansea SA2 8PP, United Kingdom, Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdomen
local.description.firstpage1583-
local.description.lastpage1604-
local.issue4-
local.volume40-
local.contributor.departmentWeierstra-Inst. Angew. Anal./S., Mohrenstr. 39, D-10117 Berlin, Germany; Department of Mathematics, Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russian Federation; Department of Mathematics, University of Wales Swansea, Swansea SA2 8PP, United Kingdom; Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdomen
local.identifier.eid2-s2.0-0141869053-
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