Reducing the phase error for finite-difference methods without increasing the order

TL;DR: In this paper, the phase error in finite-difference (FD) methods is related to the spatial resolution and thus limits the maximum grid size for a desired accuracy, which is typically achieved by defining finer resolutions or implementing higher order methods.

Abstract: The phase error in finite-difference (FD) methods is related to the spatial resolution and thus limits the maximum grid size for a desired accuracy. Greater accuracy is typically achieved by defining finer resolutions or implementing higher order methods. Both these techniques require more memory and longer computation times. In this paper, new modified methods are presented which are optimized to problems of electromagnetics. Simple methods are presented that reduce numerical phase error without additional processing time or memory requirements. Furthermore, these methods are applied to both the Helmholtz equation in the frequency domain and the finite-difference time-domain (FDTD) method. Both analytical and numerical results are presented to demonstrate the accuracy of these new methods.