Quantification of the truncation errors in finite-difference time-domain methods

To characterize a finite-difference time-domain (FDTD) scheme, the truncation error using Taylor´s series and the numerical dispersion are often used. Truncation error analysis determines the order of accuracy, but cannot differentiate one scheme from another if they have the same order of accuracy. The theoretical relation for the numerical dispersion sometimes may be difficult to obtain. This paper introduces another way to characterize the error of an FDTD scheme quantitatively. This is the truncation error with plane wave propagation. The analytical expressions for such truncation errors for Yee ´s FDTD and Crank-Nicolson FDTD are derived, and the errors are compared.