A comment on the arguments about the reliability and convergence of chaotic simulations

Abstract

Yao and Hughes commented (Tellus-A, 60: 803 - 805, 2008) that "all chaotic responses are simply numerical noise and have nothing to do with the solutions of differential equations". However, using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm of the so-called "Clean Numerical Simulation" (CNS) based on the 3500th-order Taylor expansion and data in 4180-digit multiple precision, one can gain reliable, convergent chaotic solution of Lorenz equation in a rather long interval [0,10000]. This supports Lorenz's optimistic viewpoint (Tellus-A, 60: 806 - 807, 2008): "numerical approximations can converge to a chaotic true solution throughout any finite range of time".

2 pages

Cited by in corpus (4)

• On the risks of using double precision in numerical simulations of spatio-temporal chaos
• On the inherent self-excited macroscopic randomness of chaotic three-body system
• The influence of numerical noises on statistics computation of chaotic dynamic systems
• Clean Numerical Simulation: A New Strategy to Obtain Reliable Solutions of Chaotic Dynamic Systems