@Article{IJNAM-22-843,
author = {Gao , LipingZhang , Xiaosong and Shi , Rengang},
title = {Numerical Analysis of the Finite Difference Time Domain Methods with High Accuracy in Time for Maxwell Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2025},
volume = {22},
number = {6},
pages = {843--859},
abstract = {<p style="text-align: justify;">In this paper, we give a rigorous analysis of the finite difference time domain (FDTD)
method with high accuracy in time (HAIT) (named HAIT-FDTD(M)) for the three dimensional
Maxwell equations, where the time discretization is based on the Taylor expansion of the form: $U^n=C^0_n + C^1_n ∆t + · · · + \frac{1}{ M!}C^M_n (∆t)^M$ to approximate the fields in time. It is proven that
the solutions of the schemes and the vectors representing the coefficients are divergence free. By
using the energy method, the numerical energy identities of HAIT-FDTD(M) with $3 ≤ M ≤ 8$ are
derived. It is then proved that these schemes are numerically and monotonically energy conserved
as the polynomial degree $M$ becomes large. With the help of the energy identities, stability
conditions for the six schemes are derived, and how to select $M$ and $∆t$ in practice is given. By
deriving error equations, we prove that the six schemes have convergence of the $M{\rm th}$ order in time
and the second order in space. Numerical experiments are provided and confirm the analysis on
free divergence, approximate energy conservation, stability, and convergence.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2025-1037},
url = {http://global-sci.org/intro/article_detail/ijnam/24296.html}
}