On the multi-domain compact finite difference relaxation method for high dimensional chaos: The nine-dimensional Lorenz system
N.J. Kouagou, P.G. Dlamini, S.M. Simelane, Alexandria Engineering Journal 59 (2020) 2617–2625.
Journal Article
| English
Author
Kouagou, N.J.;
Dlamini, P.G.;
Simelane, S.M.
Abstract
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.
Keywords
Publishing Year
Journal Title
Alexandria Engineering Journal
Volume
59
Issue
4
Page
2617-2625
ISSN
LibreCat-ID
Cite this
Kouagou NJ, Dlamini PG, Simelane SM. On the multi-domain compact finite difference relaxation method for high dimensional chaos: The nine-dimensional Lorenz system. Alexandria Engineering Journal. 2020;59(4):2617-2625. doi:https://doi.org/10.1016/j.aej.2020.04.025
Kouagou, N. J., Dlamini, P. G., & Simelane, S. M. (2020). On the multi-domain compact finite difference relaxation method for high dimensional chaos: The nine-dimensional Lorenz system. Alexandria Engineering Journal, 59(4), 2617–2625. https://doi.org/10.1016/j.aej.2020.04.025
@article{Kouagou_Dlamini_Simelane_2020, title={On the multi-domain compact finite difference relaxation method for high dimensional chaos: The nine-dimensional Lorenz system}, volume={59}, DOI={https://doi.org/10.1016/j.aej.2020.04.025}, number={4}, journal={Alexandria Engineering Journal}, author={Kouagou, N.J. and Dlamini, P.G. and Simelane, S.M.}, year={2020}, pages={2617–2625} }
Kouagou, N.J., P.G. Dlamini, and S.M. Simelane. “On the Multi-Domain Compact Finite Difference Relaxation Method for High Dimensional Chaos: The Nine-Dimensional Lorenz System.” Alexandria Engineering Journal 59, no. 4 (2020): 2617–25. https://doi.org/10.1016/j.aej.2020.04.025.
N. J. Kouagou, P. G. Dlamini, and S. M. Simelane, “On the multi-domain compact finite difference relaxation method for high dimensional chaos: The nine-dimensional Lorenz system,” Alexandria Engineering Journal, vol. 59, no. 4, pp. 2617–2625, 2020, doi: https://doi.org/10.1016/j.aej.2020.04.025.
Kouagou, N. J., et al. “On the Multi-Domain Compact Finite Difference Relaxation Method for High Dimensional Chaos: The Nine-Dimensional Lorenz System.” Alexandria Engineering Journal, vol. 59, no. 4, 2020, pp. 2617–25, doi:https://doi.org/10.1016/j.aej.2020.04.025.
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