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...

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Auteur principal:	Boje Edward
Format:	article
Langue:	EN FR
Publié:	EDP Sciences 2021
Sujets:	Engineering (General). Civil engineering (General) TA1-2040
Accès en ligne:	https://doaj.org/article/f6b13991ca80422f951a82dcc22a7a16
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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

Representation of simulation errors in single step methods using state dependent noise

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