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We previously described a high-accuracy version of the Yee algorithm that uses second-order nonstandard finite differences (NSFDs) and demonstrated its accuracy numerically. We now prove that at fixed frequency and grid spacing h, the leading error term is O(h6) versus O(h2) for the ordinary Yee algorithm with standard finite differences (SFDs). We numerically verify the superior accuracy of the NSFD algorithm by simulating near-field Mie scattering on a coarse grid and comparing with the SFD one and with analytical solutions. We present an updated stability analysis and show that the maximum time step for the NSFD algorithm is 20% longer than the SFD time step in two dimensions, and 36% longer in three dimensions. Finally, parameters that were previously given numerically are now analytically defined.