SIAM Journal on Numerical Analysis, Volume 59, Issue 4, Page 1857-1874, January 2021.
Pseudospectral (PS) methods are widely used for solving partial differential equations (PDEs) to high accuracy in simple geometries. They can be seen as the limit of finite difference methods for increasing order of accuracy. Similarly, recently introduced Hermite-based finite difference approximations converge to Hermite-based pseudospectral (HPS) limits. We derive here HPS coefficients and make comparisons between PS and HPS approximations. Using half the number of nodes and twice the amount of data per node, HPS approximations match the accuracy of the PS method. A potential advantage of HPS over PS arises when a computer has multiple cores available.

中文翻译：

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基于 Hermite 的有限差分格式的无限阶极限

SIAM 数值分析期刊，第 59 卷，第 4 期，第 1857-1874 页，2021 年 1 月。
伪谱 (PS) 方法广泛用于求解简单几何中的高精度偏微分方程 (PDE)。它们可以被看作是提高精度的有限差分方法的极限。类似地，最近引入的基于 Hermite 的有限差分近似收敛到基于 Hermite 的伪谱 (HPS) 限制。我们在这里推导出 HPS 系数并在 PS 和 HPS 近似值之间进行比较。使用一半的节点数和两倍的每个节点的数据量，HPS 近似与 PS 方法的准确性相匹配。当计算机具有多个可用内核时，HPS 相对于 PS 的潜在优势就出现了。