Round-off Error Analysis of Explicit One-Step Numerical Integration Methods

Sylvie Boldo 1 Florian Faissole 1 Alexandre Chapoutot 2
1 TOCCATA - Certified Programs, Certified Tools, Certified Floating-Point Computations
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
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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Communication dans un congrès
24th IEEE Symposium on Computer Arithmetic, Jul 2017, London, United Kingdom. 〈http://arith24.arithsymposium.org/〉. 〈10.1109/ARITH.2017.22〉
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Dernière modification le : vendredi 27 avril 2018 - 14:40:07

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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. 〈http://arith24.arithsymposium.org/〉. 〈10.1109/ARITH.2017.22〉. 〈hal-01581794〉

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