On the multi-domain compact finite difference relaxation method for high dimensional chaos: The nine-dimensional Lorenz system

In this paper, we implement the multidomain compact finite difference method to numerically study high dimensional chaos by considering the nine-dimensional Lorenz system. Most of the existing numerical methods converge slowly for this kind of problems and this results in inaccurate approximations....

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Bibliographic Details
Published inAlexandria engineering journal Vol. 59; no. 4; pp. 2617 - 2625
Main Authors Kouagou, J.N., Dlamini, P.G., Simelane, S.M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2020
Elsevier
Subjects
9D Lorenz system
Compact finite difference
Multidomain
9D Lorenz system
Multidomain
Compact finite difference
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Summary:In this paper, we implement the multidomain compact finite difference method to numerically study high dimensional chaos by considering the nine-dimensional Lorenz system. Most of the existing numerical methods converge slowly for this kind of problems and this results in inaccurate approximations. Though highly accurate, the compact finite difference method becomes less accurate for problems characterized by chaotic solutions, even with an increase in the number of grid points. As a result, in this work, we adopt the multidomain approach. This approach remarkably improves the results as well as the efficiency of the method.
ISSN:1110-0168
DOI:10.1016/j.aej.2020.04.025