The Hermite-Taylor method, introduced in 2005 by Goodrich, Hagstrom and Lorenz, is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfortunately its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor Correction Function method, which provides exactly such a systematic approach for handing boundary conditions. Here we focus on Maxwell's equations but note that the method is easily extended to other hyperbolic problems.

翻译：Hermite-Taylor方法是由Goodrich、Hagstrom和Lorenz于2005年提出的，适用于周期域上的线性双曲系统，具有高效和精确的优点。然而，缺乏一种系统的方法来处理边界条件阻止了其广泛应用。本文提出了Hermite-Taylor校正函数方法，为处理边界条件提供了一种系统的方法。本文重点介绍了Maxwell方程，但该方法易于扩展到其他双曲问题。