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Conference Papers Year : 2017

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.
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Dates and versions

hal-01581794 , version 1 (05-09-2017)

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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⟩
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