@article{Zhang2023, 
author = {Li Zhang and Maohua Ran and Hanyue Zhang},
title = {Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {264-284},
keywords = {Maxwell's equations, ADI-FDTD, energy method, approximately energy-preserving},
url = {https://www.sciopen.com/article/10.3934/math.2023012},
doi = {10.3934/math.2023012},
abstract = {In this work, the ADI-FDTD method with fourth-order accuracy in time for the 2-D Maxwell's equations without sources and charges is proposed. We mainly focus on energy analysis of the proposed ADI-FDTD method. By using the energy method, we derive the numerical energy identity of the ADI-FDTD method and show that the ADI-FDTD method is approximately energy-preserving. In comparison with the energy in theory, the numerical one has two perturbation terms and can be used in computation in order to keep it approximately energy-preserving. Numerical experiments are given to show the performance of the proposed ADI-FDTD method which confirm the theoretical results.}
}