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 numer-ically 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 inac-curate 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 remark-ably improves the results as well as the efficiency of the method.(C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).