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Round-off error and exceptional behavior analysis of explicit Runge-Kutta methods

Abstract : Numerical integration schemes are mandatory to understand complex behaviors of dynamical systems described by ordinary differential equations. Implementation of these numerical methods involve floating-point computations and propagation of round-off errors. This paper presents a new fine-grained analysis of round-off errors in explicit Runge-Kutta integration methods, taking into account exceptional behaviors, such as underflow and overflow. Linear stability properties play a central role in the proposed approach. For a large class of Runge-Kutta methods applied on linear problems, a tight bound of the round-off errors is provided. A simple test is defined and ensures the absence of underflow and a tighter round-off error bound. The absence of overflow is guaranteed as linear stability properties imply that (computed) solutions are non-increasing.
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Submitted on : Monday, September 16, 2019 - 9:35:42 AM
Last modification on : Friday, July 8, 2022 - 10:06:34 AM
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Sylvie Boldo, Florian Faissole, Alexandre Chapoutot. Round-off error and exceptional behavior analysis of explicit Runge-Kutta methods. IEEE Transactions on Computers, 2019, ⟨10.1109/TC.2019.2917902⟩. ⟨hal-01883843v3⟩



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