On the relation between reliable computation time, float-point precision and the Lyapunov exponent in chaotic systems
arXiv:1410.49191.25 citations
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Provides a quantitative tool for predicting simulation reliability in chaotic dynamics, relevant to computational scientists and physicists.
The paper derives a theoretical relation Tc = (lnB/λ)K + C linking reliable computation time, floating-point precision, and Lyapunov exponent in chaotic systems, and validates it numerically with good agreement.
The relation among reliable computation time, Tc, float-point precision, K, and the Lyapunov exponent, λ, is obtained as Tc= (lnB/λ)K+C, where B is the base of the float-point system and C is a constant dependent only on the chaotic equation. The equation shows good agreement with numerical experimental results, especially the scale factors.