Numerical analysis of Finite-Difference Time-Domain method for 2D/3D Maxwell's equations in a Cole-Cole dispersive medium

Two efficient numerical schemes based on L1 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 O((Delta t)(2-alpha) + (Delta x)(2) + (Delta y)(2)), where Delta t, Delta x, Delta y are respectively the step sizes in time, space in x-and y-direction. The parameter a is a measure of the dispersion broadening. Numerical experiments are performed to confirm our theoretical analysis.