Pseudospectral Time Domain Method Implementation Using Finite Difference Time Stepping

Lagrange interpolation polynomials-based Chebyshev pseudospectral time domain (CPSTD) method is an efficient time domain solver for Maxwell equations. Although it has the lowest interpolation error among pseudospectral time domain methods, time derivatives must be calculated using higher order time derivative schemes, such as the Runge–Kutta method. The higher order time derivative methods slow down the computation speed at each step by several folds. In this letter, we show that central finite differences can be used for implementation of time derivatives in CPSTD method. Results are verified by a resonator problem.