Representation of simulation errors in single step methods using state dependent noise
The local error of single step methods is modelled as a function of the state derivative multiplied by bias and zero-mean white noise terms. The deterministic Taylor series expansion of the local error depends on the state derivative meaning that the local error magnitude is zero in steady state and...
Guardado en:
Autor principal: | |
---|---|
Formato: | article |
Lenguaje: | EN FR |
Publicado: |
EDP Sciences
2021
|
Materias: | |
Acceso en línea: | https://doaj.org/article/f6b13991ca80422f951a82dcc22a7a16 |
Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
id |
oai:doaj.org-article:f6b13991ca80422f951a82dcc22a7a16 |
---|---|
record_format |
dspace |
spelling |
oai:doaj.org-article:f6b13991ca80422f951a82dcc22a7a162021-12-02T17:13:35ZRepresentation of simulation errors in single step methods using state dependent noise2261-236X10.1051/matecconf/202134700001https://doaj.org/article/f6b13991ca80422f951a82dcc22a7a162021-01-01T00:00:00Zhttps://www.matec-conferences.org/articles/matecconf/pdf/2021/16/matecconf_sacam21_00001.pdfhttps://doaj.org/toc/2261-236XThe local error of single step methods is modelled as a function of the state derivative multiplied by bias and zero-mean white noise terms. The deterministic Taylor series expansion of the local error depends on the state derivative meaning that the local error magnitude is zero in steady state and grows with the rate of change of the state vector. The stochastic model of the local error may include a constant, “catch-all” noise term. A continuous time extension of the local error model is developed and this allows the original continuous time state differential equation to be represented by a combination of the simulation method and a stochastic term. This continuous time stochastic differential equation model can be used to study the propagation of the simulation error in Monte Carlo experiments, for step size control, or for propagating the mean and variance. This simulation error model can be embedded into continuous-discrete state estimation algorithms. Two illustrative examples are included to highlight the application of the approach.Boje EdwardEDP SciencesarticleEngineering (General). Civil engineering (General)TA1-2040ENFRMATEC Web of Conferences, Vol 347, p 00001 (2021) |
institution |
DOAJ |
collection |
DOAJ |
language |
EN FR |
topic |
Engineering (General). Civil engineering (General) TA1-2040 |
spellingShingle |
Engineering (General). Civil engineering (General) TA1-2040 Boje Edward Representation of simulation errors in single step methods using state dependent noise |
description |
The local error of single step methods is modelled as a function of the state derivative multiplied by bias and zero-mean white noise terms. The deterministic Taylor series expansion of the local error depends on the state derivative meaning that the local error magnitude is zero in steady state and grows with the rate of change of the state vector. The stochastic model of the local error may include a constant, “catch-all” noise term.
A continuous time extension of the local error model is developed and this allows the original continuous time state differential equation to be represented by a combination of the simulation method and a stochastic term. This continuous time stochastic differential equation model can be used to study the propagation of the simulation error in Monte Carlo experiments, for step size control, or for propagating the mean and variance. This simulation error model can be embedded into continuous-discrete state estimation algorithms.
Two illustrative examples are included to highlight the application of the approach. |
format |
article |
author |
Boje Edward |
author_facet |
Boje Edward |
author_sort |
Boje Edward |
title |
Representation of simulation errors in single step methods using state dependent noise |
title_short |
Representation of simulation errors in single step methods using state dependent noise |
title_full |
Representation of simulation errors in single step methods using state dependent noise |
title_fullStr |
Representation of simulation errors in single step methods using state dependent noise |
title_full_unstemmed |
Representation of simulation errors in single step methods using state dependent noise |
title_sort |
representation of simulation errors in single step methods using state dependent noise |
publisher |
EDP Sciences |
publishDate |
2021 |
url |
https://doaj.org/article/f6b13991ca80422f951a82dcc22a7a16 |
work_keys_str_mv |
AT bojeedward representationofsimulationerrorsinsinglestepmethodsusingstatedependentnoise |
_version_ |
1718381356730286080 |