Skip to Main content Skip to Navigation
Conference papers

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.
Document type :
Conference papers
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download
Contributor : Florian Faissole Connect in order to contact the contributor
Submitted on : Tuesday, September 5, 2017 - 10:25:10 AM
Last modification on : Friday, December 3, 2021 - 11:34:11 AM


Files produced by the author(s)



Sylvie Boldo, Florian Faissole, Alexandre Chapoutot. Round-off Error Analysis of Explicit One-Step Numerical Integration Methods. 24th IEEE Symposium on Computer Arithmetic, Jul 2017, London, United Kingdom. ⟨10.1109/ARITH.2017.22⟩. ⟨hal-01581794⟩



Record views


Files downloads