There is a need for an accurate optical simulation tool for liquid crystal structures with director variations in more than one dimension. Finite-difference time-domain (FDTD) computation of Maxwell's equations is one approach to consider. The FDTD method has been in use in the electrical engineering community for years, but has only recently been applied to liquid crystal structures. Little is known about the accuracy of FDTD simulations of typical liquid crystal structures, in which the dielectric tensor can undergo large local spatial variations. This paper compares FDTD simulations and analytic solutions of two liquid crystal problems: the twisted-nematic cell and Bragg reflection from a planar cholesteric layer.