---
_id: '45785'
abstract:
- lang: eng
  text: 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.
author:
- first_name: N.J.
  full_name: Kouagou, N.J.
  last_name: Kouagou
- first_name: P.G.
  full_name: Dlamini, P.G.
  last_name: Dlamini
- first_name: S.M.
  full_name: Simelane, S.M.
  last_name: Simelane
citation:
  ama: 'Kouagou NJ, Dlamini PG, Simelane SM. On the multi-domain compact finite difference
    relaxation method for high dimensional chaos: The nine-dimensional Lorenz system.
    <i>Alexandria Engineering Journal</i>. 2020;59(4):2617-2625. doi:<a href="https://doi.org/10.1016/j.aej.2020.04.025">https://doi.org/10.1016/j.aej.2020.04.025</a>'
  apa: 'Kouagou, N. J., Dlamini, P. G., &#38; Simelane, S. M. (2020). On the multi-domain
    compact finite difference relaxation method for high dimensional chaos: The nine-dimensional
    Lorenz system. <i>Alexandria Engineering Journal</i>, <i>59</i>(4), 2617–2625.
    <a href="https://doi.org/10.1016/j.aej.2020.04.025">https://doi.org/10.1016/j.aej.2020.04.025</a>'
  bibtex: '@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={<a href="https://doi.org/10.1016/j.aej.2020.04.025">https://doi.org/10.1016/j.aej.2020.04.025</a>},
    number={4}, journal={Alexandria Engineering Journal}, author={Kouagou, N.J. and
    Dlamini, P.G. and Simelane, S.M.}, year={2020}, pages={2617–2625} }'
  chicago: '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.” <i>Alexandria Engineering Journal</i> 59, no. 4 (2020): 2617–25.
    <a href="https://doi.org/10.1016/j.aej.2020.04.025">https://doi.org/10.1016/j.aej.2020.04.025</a>.'
  ieee: '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,” <i>Alexandria Engineering Journal</i>, vol. 59, no. 4, pp. 2617–2625,
    2020, doi: <a href="https://doi.org/10.1016/j.aej.2020.04.025">https://doi.org/10.1016/j.aej.2020.04.025</a>.'
  mla: 'Kouagou, N. J., et al. “On the Multi-Domain Compact Finite Difference Relaxation
    Method for High Dimensional Chaos: The Nine-Dimensional Lorenz System.” <i>Alexandria
    Engineering Journal</i>, vol. 59, no. 4, 2020, pp. 2617–25, doi:<a href="https://doi.org/10.1016/j.aej.2020.04.025">https://doi.org/10.1016/j.aej.2020.04.025</a>.'
  short: N.J. Kouagou, P.G. Dlamini, S.M. Simelane, Alexandria Engineering Journal
    59 (2020) 2617–2625.
date_created: 2023-06-27T10:25:45Z
date_updated: 2023-06-27T10:28:56Z
doi: https://doi.org/10.1016/j.aej.2020.04.025
extern: '1'
intvolume: '        59'
issue: '4'
keyword:
- Multidomain
- Compact finite difference
- 9D Lorenz system
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.sciencedirect.com/science/article/pii/S1110016820301769
oa: '1'
page: 2617-2625
publication: Alexandria Engineering Journal
publication_identifier:
  issn:
  - 1110-0168
related_material:
  record:
  - id: '45785'
    relation: earlier_version
    status: private
status: public
title: 'On the multi-domain compact finite difference relaxation method for high dimensional
  chaos: The nine-dimensional Lorenz system'
type: journal_article
user_id: '87189'
volume: 59
year: '2020'
...