Low rank Runge–Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise
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| Title: | Low rank Runge–Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise |
|---|---|
| Authors: | Burrage, Kevin1,2, Burrage, Pamela M.3 pamela.burrage@qut.edu.au |
| Source: | Journal of Computational & Applied Mathematics. Oct2012, Vol. 236 Issue 16, p3920-3930. 11p. |
| Subjects: | Runge-Kutta formulas, Stochastic analysis, Hamiltonian systems, Performance evaluation, Numerical analysis, Mathematical analysis |
| Abstract: | Abstract: In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM () methods to construct symplectic Runge–Kutta methods for all values of and with . However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge–Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule. [Copyright &y& Elsevier] |
| Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 76313199 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Low rank Runge–Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Burrage%2C+Kevin%22">Burrage, Kevin</searchLink><relatesTo>1,2</relatesTo><br /><searchLink fieldCode="AR" term="%22Burrage%2C+Pamela+M%2E%22">Burrage, Pamela M.</searchLink><relatesTo>3</relatesTo><i> pamela.burrage@qut.edu.au</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+%26+Applied+Mathematics%22">Journal of Computational & Applied Mathematics</searchLink>. Oct2012, Vol. 236 Issue 16, p3920-3930. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Runge-Kutta+formulas%22">Runge-Kutta formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+analysis%22">Stochastic analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Hamiltonian+systems%22">Hamiltonian systems</searchLink><br /><searchLink fieldCode="DE" term="%22Performance+evaluation%22">Performance evaluation</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM () methods to construct symplectic Runge–Kutta methods for all values of and with . However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge–Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.cam.2012.03.007 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 3920 Subjects: – SubjectFull: Runge-Kutta formulas Type: general – SubjectFull: Stochastic analysis Type: general – SubjectFull: Hamiltonian systems Type: general – SubjectFull: Performance evaluation Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Mathematical analysis Type: general Titles: – TitleFull: Low rank Runge–Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Burrage, Kevin – PersonEntity: Name: NameFull: Burrage, Pamela M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2012 Type: published Y: 2012 Identifiers: – Type: issn-print Value: 03770427 Numbering: – Type: volume Value: 236 – Type: issue Value: 16 Titles: – TitleFull: Journal of Computational & Applied Mathematics Type: main |
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