Integration of the stochastic underdamped harmonic oscillator by the θ-method

[EN]In recent papers, a simple harmonic oscillator with additive noise has been studied by several researchers, and it has been shown that its mean total energy increases linearly as time goes to infinity. In contrast to them, we consider an underdamped harmonic oscillator with additive noise. Our a...

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Autores: Tocino García, Ángel Andrés, Komori, Y., Mitsui, T.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/160899
Acceso en línea:http://hdl.handle.net/10366/160899
Access Level:acceso abierto
Palabra clave:Stochastic differential equations
Stochastic underdamped oscillator
Stochastic theta methods
Second order moment
Numerical methods
Numerical integration
Ecuaciones diferenciales estocásticas
Procesos estocásticos
Integración numérica
1202.13 Análisis Armónico
1201.04 Álgebra Diferencial
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spelling Integration of the stochastic underdamped harmonic oscillator by the θ-methodTocino García, Ángel AndrésKomori, Y.Mitsui, T.Stochastic differential equationsStochastic underdamped oscillatorStochastic theta methodsSecond order momentNumerical methodsNumerical integrationEcuaciones diferenciales estocásticasProcesos estocásticosIntegración numérica1202.13 Análisis Armónico1201.04 Álgebra Diferencial[EN]In recent papers, a simple harmonic oscillator with additive noise has been studied by several researchers, and it has been shown that its mean total energy increases linearly as time goes to infinity. In contrast to them, we consider an underdamped harmonic oscillator with additive noise. Our analysis reveals that the mean total energy of the stochastic underdamped harmonic oscillator remains bounded and it asymptotically tends to a certain value. In addition, we give a relation between the mean kinetic energy and the growth rate of the mean total energy. Whereas all stochastic -methods preserve this relation as they are of weak second local order, we show that only the stochastic trapezoidal method can attain the asymptotic values of the mean total energy and its derivative given by the exact solution. Numerical experiments are carried out to confirm these results.Publicación en abierto financiada por la Universidad de Salamanca como participante en el Acuerdo Transformativo CRUE-CSIC con Elsevier, 2021-2024Elsevier202420242022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10366/160899reponame:GREDOS. Repositorio Institucional de la Universidad de Salamancainstname:Universidad de Salamanca (USAL)InglésAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:gredos.usal.es:10366/1608992026-06-07T06:28:51Z
dc.title.none.fl_str_mv Integration of the stochastic underdamped harmonic oscillator by the θ-method
title Integration of the stochastic underdamped harmonic oscillator by the θ-method
spellingShingle Integration of the stochastic underdamped harmonic oscillator by the θ-method
Tocino García, Ángel Andrés
Stochastic differential equations
Stochastic underdamped oscillator
Stochastic theta methods
Second order moment
Numerical methods
Numerical integration
Ecuaciones diferenciales estocásticas
Procesos estocásticos
Integración numérica
1202.13 Análisis Armónico
1201.04 Álgebra Diferencial
title_short Integration of the stochastic underdamped harmonic oscillator by the θ-method
title_full Integration of the stochastic underdamped harmonic oscillator by the θ-method
title_fullStr Integration of the stochastic underdamped harmonic oscillator by the θ-method
title_full_unstemmed Integration of the stochastic underdamped harmonic oscillator by the θ-method
title_sort Integration of the stochastic underdamped harmonic oscillator by the θ-method
dc.creator.none.fl_str_mv Tocino García, Ángel Andrés
Komori, Y.
Mitsui, T.
author Tocino García, Ángel Andrés
author_facet Tocino García, Ángel Andrés
Komori, Y.
Mitsui, T.
author_role author
author2 Komori, Y.
Mitsui, T.
author2_role author
author
dc.subject.none.fl_str_mv Stochastic differential equations
Stochastic underdamped oscillator
Stochastic theta methods
Second order moment
Numerical methods
Numerical integration
Ecuaciones diferenciales estocásticas
Procesos estocásticos
Integración numérica
1202.13 Análisis Armónico
1201.04 Álgebra Diferencial
topic Stochastic differential equations
Stochastic underdamped oscillator
Stochastic theta methods
Second order moment
Numerical methods
Numerical integration
Ecuaciones diferenciales estocásticas
Procesos estocásticos
Integración numérica
1202.13 Análisis Armónico
1201.04 Álgebra Diferencial
description [EN]In recent papers, a simple harmonic oscillator with additive noise has been studied by several researchers, and it has been shown that its mean total energy increases linearly as time goes to infinity. In contrast to them, we consider an underdamped harmonic oscillator with additive noise. Our analysis reveals that the mean total energy of the stochastic underdamped harmonic oscillator remains bounded and it asymptotically tends to a certain value. In addition, we give a relation between the mean kinetic energy and the growth rate of the mean total energy. Whereas all stochastic -methods preserve this relation as they are of weak second local order, we show that only the stochastic trapezoidal method can attain the asymptotic values of the mean total energy and its derivative given by the exact solution. Numerical experiments are carried out to confirm these results.
publishDate 2022
dc.date.none.fl_str_mv 2022
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10366/160899
url http://hdl.handle.net/10366/160899
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname:Universidad de Salamanca (USAL)
instname_str Universidad de Salamanca (USAL)
reponame_str GREDOS. Repositorio Institucional de la Universidad de Salamanca
collection GREDOS. Repositorio Institucional de la Universidad de Salamanca
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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