Comment on “Computational periodicity as observed in a simple system,” by Edward N. Lorenz (2006a)

Lun-Shin Yao; Dan Hughes

doi:10.1111/j.1600-0870.2008.00301.x

Comment on “Computational periodicity as observed in a simple system,” by Edward N. Lorenz (2006a)

Tellus

Volume 60 (2008): Issue 4

By: Lun-Shin Yao and Dan Hughes

Open Access

|Jan 2008

Abstract

Systems of ordinary differential equations that exhibit chaotic responses have yet to be correctly integrated. So far no ‘convergent’ computational results have been determined for chaotic differential equations. Various computed numbers are not solutions of the continuous differential equations; all chaotic responses are simply numerical noise and have nothing to do with the solutions of differential equations. It would be an exciting contribution if a convergent computed chaotic solution for a Lorenz model could be obtained.

References

Ascher , U. M. and Petzold , L. R., 1998 . Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations , Society for Industrial and Applied Mathematics , SIAM , New York .
Search in Google Scholar Back to article
Cloutman , L. D., 1996 . A Note on the Stability and Accuracy of Finite Difference Approximations to Differential Equations. Lawrence Liv-ermore National Laboratory, UCRL-ID-125549.
Search in Google Scholar Back to article
Cloutman , L. D., 1998 . Chaos and Instabilities in Finite Difference Ap-proximations to Nonlinear Differential Equations. Lawrence Liver-more National Laboratory, UCRL-ID-131333.
Search in Google Scholar Back to article
Lorenz , E. N., 1963 . Deterministic nonperiodic flow . J. Atmos. Sci . 20 , 130 – 141 .
Search in Google Scholar Back to article
Lorenz , E. N., 1990 . Can chaos and intransitivity lead to interannual variability? Tellus 42A , 378 – 389 .
Search in Google Scholar Back to article
Lorenz , E. N., 2006a . Computational periodicity as observed in a simple system . Tellus 58A , 549 – 557 .
Search in Google Scholar Back to article
Lorenz , E. N., 2006b . An attractor embedded in the atmosphere . Tellus 58A , 425 – 429 .
Search in Google Scholar Back to article
Pielke , R. A. and Zeng , X., 1994 . Long-term variability of climate . J. Atmos. Sci . 51 ( 1 ), 155 – 159 .
Search in Google Scholar Back to article
Press , W. H. , Flannery , B. P. , Teukolsky , S. A. and Vettering , W. T., 1986 . Numerical Recipes ; The Art of Scientific Computing, Cambridge University Press, Cambridge.
Search in Google Scholar Back to article
Teixeira , J. , Reynolds , C. A. and Judd , K., 2007 . Time step sensitivity of nonlinear atmospheric models: numerical convergence, truncation error growth, and ensemble design . J. Atmos. Sci . 64 , 175 – 189 .
Search in Google Scholar Back to article
Viana M., 2000 . What’s new on Lorenz strange attractors? Math. Intell . 22 , 6 – 19 .
Search in Google Scholar Back to article
Yao , L. S., 2005 . Computed chaos or numerical errors. online manuscript, http://arxiv.orgiabsinlin.CD/0506045.
Search in Google Scholar Back to article
Yao , L. S. and Hughes , D., 2007 . Comment on, “time step sensitivity of nonlinear atmospheric models: numerical convergence, truncation error growth, and ensemble design” . J. Atmos. Sci ., 65 ( 2 ), 681 – 682 .
Search in Google Scholar Back to article
Young , C., 1966 . Comment on “deterministic nonperiodic flow . ” J. At-mos. Sci . 23 , 628 – 629 .
Search in Google Scholar Back to article