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.

中文翻译：

---

高维混沌的多域紧致有限差分松弛方法：九维Lorenz系统

在本文中，我们通过考虑九维Lorenz系统，实现了多域紧凑有限差分方法来对高维混沌进行数值研究。对于这种问题，大多数现有的数值方法收敛缓慢，这导致近似值不准确。尽管精确度很高，但紧凑的有限差分方法对于以混沌解为特征的问题的准确性降低，即使增加了网格点的数量也是如此。因此，在这项工作中，我们采用了多域方法。该方法显着改善了结果以及方法的效率。