The Hermite-Taylor Correction Function Method for Maxwell’s Equations

doi:10.1007/s42967-023-00287-5

Abstract

Abstract: The Hermite-Taylor method, introduced in 2005 by Goodrich et al. 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 (CFM), which provides exactly such a systematic approach for handling boundary conditions. Here we focus on Maxwell’s equations but note that the method is easily extended to other hyperbolic problems.

Key words: Hermite method, Correction function method (CFM), Maxwell's equations, High order, Boundary conditions

CLC Number:

35Q61
65M70

Yann-Meing Law, Daniel Appel?. The Hermite-Taylor Correction Function Method for Maxwell’s Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(1): 347-371.

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