Can We Obtain a Reliable Convergent Chaotic Solution in any Given Finite Interval of Time?

Shijun Liao
2014 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
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
more » ... g 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".
doi:10.1142/s0218127414501193 fatcat:l6c7vtb4cvbxvmevvruxqd2xs4