Two efficient numerical schemes based on $\mathcal{L}1$ formula and Finite-Difference Time-Domain (FDTD) method are constructed for Maxwell's equations in a Cole-Cole dispersive medium. The temporal discretizations are built upon the leap-frog method and Crank-Nicolson method, respectively. We carry out the energy stability and error analysis rigorously by the energy method. Both schemes have been proved convergence with order $\mathcal{O}({(\mathrm{\Delta }t)}^{2-\alpha }+{(\mathrm{\Delta }x)}^2+{(\mathrm{\Delta }y)}^2)$, where $\mathrm{\Delta }t,\mathrm{\Delta }x,\mathrm{\Delta }y$ are respectively the step sizes in time, space in x- and y-direction. The parameter α is a measure of the dispersion broadening. Numerical experiments are performed to confirm our theoretical analysis.

基于两种有效的数值方案 $\mathcal{大号}\mathrm{1个}$在Cole-Cole色散介质中，为Maxwell方程构造了公式和有限差分时域（FDTD）方法。时间离散化分别建立在跳越方法和Crank-Nicolson方法上。我们通过能量方法严格进行能量稳定性和误差分析。两种方案都被证明具有阶收敛性$\mathcal{Ø}（{（\mathrm{\Delta }Ť）}^{\mathrm{2个}-\alpha }+{（\mathrm{\Delta }X）}^{\mathrm{2个}}+{（\mathrm{\Delta }ÿ）}^{\mathrm{2个}}）$， 在哪里 $\mathrm{\Delta }Ť，\mathrm{\Delta }X，\mathrm{\Delta }ÿ$分别是时间步长，在x和y方向上的间隔。参数α是色散展宽的量度。进行数值实验以证实我们的理论分析。