While the alternating-direction implicit finitedifference time-domain (ADI-FDTD) method preserves the second-order temporal accuracy of the conventional FDTD technique, the locally one-dimensional (LOD)-FDTD method exhibits a first-order in time splitting error. Despite this difference, the numerical dispersion analyses of these methods reveal that both present similar accuracy properties. For this reason, the characteristic non-commutativity error of the LOD-FDTD scheme has not received much

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... tention. In this work, we determine the closed form of the local truncation error for the 3D-LOD-FDTD scheme. We find that it presents error terms which depend on the time-step size multiplied by the spatial derivatives of the fields. Numerical results confirm that these terms become a significant source of error which is not revealed in the dispersion analyses. Index Terms-Alternating direction implicit split-step FDTD methods, local truncation error, locally one-dimensional FDTD method, numerical dispersion.