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：埃尔米特-泰勒方法由Goodrich、Hagstrom和Lorenz于2005年提出，在周期域上应用于线性双曲系统时具有极高的效率和精度。遗憾的是，由于缺乏系统性的边界条件实现方法，该方法未能得到广泛应用。本文提出埃尔米特-泰勒修正函数法，为处理边界条件提供了精确的系统性方案。本文重点探讨麦克斯韦方程的应用，但需指出该方法可轻松推广至其他双曲问题。