Round-off error analysis of explicit one-step numerical integration methods

Sylvie Boldo; Florian Faissole; Alexandre Chapoutot

doi:10.1109/ARITH.2017.22

Round-off error analysis of explicit one-step numerical integration methods

Sylvie Boldo
, Florian Faissole
, Alexandre Chapoutot

Université Paris-Saclay
Centre national de la recherche scientifique
ENSTA ParisTech

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Citations (Scopus)

Abstract

Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off errors occur. In order to guarantee their accuracy, we aim at providing bounds on the round-off errors of explicit one-step numerical integration methods. Our methodology is to apply a fine-grained analysis to these numerical algorithms. Our originality is that our floating-point analysis takes advantage of the linear stability of the scheme, a mathematical property that vouches the scheme is well-behaved.

Original language	English
Title of host publication	Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017
Editors	Florent de Dinechin, Neil Burgess, Javier Bruguera
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	82-89
Number of pages	8
ISBN (Electronic)	9781538619643
DOIs	https://doi.org/10.1109/ARITH.2017.22
Publication status	Published - 30 Aug 2017
Externally published	Yes
Event	24th IEEE Symposium on Computer Arithmetic, ARITH 2017 - London, United Kingdom Duration: 24 Jul 2017 → 26 Jul 2017

Publication series

Name	Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017

Conference

Conference	24th IEEE Symposium on Computer Arithmetic, ARITH 2017
Country/Territory	United Kingdom
City	London
Period	24/07/17 → 26/07/17

Access to Document

10.1109/ARITH.2017.22

Cite this

Boldo, S., Faissole, F., & Chapoutot, A. (2017). Round-off error analysis of explicit one-step numerical integration methods. In F. de Dinechin, N. Burgess, & J. Bruguera (Eds.), Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017 (pp. 82-89). Article 8023070 (Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ARITH.2017.22

Boldo, Sylvie ; Faissole, Florian ; Chapoutot, Alexandre. / Round-off error analysis of explicit one-step numerical integration methods. Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017. editor / Florent de Dinechin ; Neil Burgess ; Javier Bruguera. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 82-89 (Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017).

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title = "Round-off error analysis of explicit one-step numerical integration methods",

abstract = "Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off errors occur. In order to guarantee their accuracy, we aim at providing bounds on the round-off errors of explicit one-step numerical integration methods. Our methodology is to apply a fine-grained analysis to these numerical algorithms. Our originality is that our floating-point analysis takes advantage of the linear stability of the scheme, a mathematical property that vouches the scheme is well-behaved.",

author = "Sylvie Boldo and Florian Faissole and Alexandre Chapoutot",

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Boldo, S, Faissole, F & Chapoutot, A 2017, Round-off error analysis of explicit one-step numerical integration methods. in F de Dinechin, N Burgess & J Bruguera (eds), Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017., 8023070, Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017, Institute of Electrical and Electronics Engineers Inc., pp. 82-89, 24th IEEE Symposium on Computer Arithmetic, ARITH 2017, London, United Kingdom, 24/07/17. https://doi.org/10.1109/ARITH.2017.22

Round-off error analysis of explicit one-step numerical integration methods. / Boldo, Sylvie; Faissole, Florian; Chapoutot, Alexandre.
Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017. ed. / Florent de Dinechin; Neil Burgess; Javier Bruguera. Institute of Electrical and Electronics Engineers Inc., 2017. p. 82-89 8023070 (Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off errors occur. In order to guarantee their accuracy, we aim at providing bounds on the round-off errors of explicit one-step numerical integration methods. Our methodology is to apply a fine-grained analysis to these numerical algorithms. Our originality is that our floating-point analysis takes advantage of the linear stability of the scheme, a mathematical property that vouches the scheme is well-behaved.

AB - Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off errors occur. In order to guarantee their accuracy, we aim at providing bounds on the round-off errors of explicit one-step numerical integration methods. Our methodology is to apply a fine-grained analysis to these numerical algorithms. Our originality is that our floating-point analysis takes advantage of the linear stability of the scheme, a mathematical property that vouches the scheme is well-behaved.

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M3 - Conference contribution

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BT - Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017

A2 - de Dinechin, Florent

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Boldo S, Faissole F, Chapoutot A. Round-off error analysis of explicit one-step numerical integration methods. In de Dinechin F, Burgess N, Bruguera J, editors, Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 82-89. 8023070. (Proceedings - 24th IEEE Symposium on Computer Arithmetic, ARITH 2017). doi: 10.1109/ARITH.2017.22

Round-off error analysis of explicit one-step numerical integration methods

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