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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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Submitted on : Tuesday, September 5, 2017 - 10:25:10 AM
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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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