Adv Comput Math
Developing and analyzing fourth-order difference
methods for the metamaterial Maxwell’s equations
· Meng Chen
· Min Chen
Received: 26 November 2017 / Accepted: 17 May 2018
© Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract In this paper, we develop both a fourth order explicit scheme and a com-
pact implicit scheme for solving the metamaterial Maxwell’s equations. A systematic
technique is introduced to prove stability and error estimate for both schemes.
Numerical results supporting our analysis are presented. To our best knowledge, our
convergence theory and stability results are novel, and provide the first error estimate
for the fourth order finite difference methods for Maxwell’s equations.
Keywords Maxwell’s equations · Metamaterial · FDTD method ·
Fourth order method
Mathematics Subject Classification (2010) 65N30 · 35L15 · 78-08
Communicated by: Aihui Zhou
Work supported by NSF grant DMS-1416742 and NSFC project 11671340.
Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School
of Mathematics and Computational Science, Xiangtan University, Xiangtan, China