The major objective of this dissertation is to design simple low-dispersion Finite-Difference Time-Domain (FDTD) methods for electromagnetics. Literature review indicated that the Nonstandard Finite Difference (NSFD) method exhibits great potentials in dispersion reduction. Different from the Standard Finite Difference (SFD) methods, the NSFD methods are derived directly based upon dispersion analysis. In this dissertation, the basic concepts of the NSFD methods are generalized to various extended finite-difference stencils. Furthermore, several improved NSFD methods are presented based on the standard fourth-order stencil to mitigate the dispersion in multi-dimensional domains. The least square method is used to optimize the coefficients of the proposed stencils. Numerical simulations show that these schemes significantly reduce the dispersion error of their standard counterparts. Many technical issues in practical implementations, such as absorbing boundary conditions, stability conditions, and Gauss's Laws, are discussed and justified. Moreover, two special conditions are proposed for the extended stencils in the vicinity of the dielectric material discontinuities. It was demonstrated that the accuracy of the fourth-order stencil is fully restored by applying these conditions.

A very important electromagnetic interference (EMI) problem is also presented in this dissertation. The problem concerns the effects of passengers on personal electronic device (PED) mutual coupling in a simplified Boeing 757 fuselage. The results predicted by FDTD are compared to the measurements performed in the Electro-Magnetic Anechoic Chamber (EMAC) of Arizona State University. It was found that the presence of the passengers significantly dampens the resonances in the fuselage, which lower the potential EMI threat to the on-board communication/navigation systems.