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This paper discusses the enhancement of numerical dispersion characteristics in the context of the finite-difference time-domain method based on a (2,4) computational stencil. Rather than implementing the conventional approach-based on Taylor analysis-for the determination of the finite-difference operators, two alternative procedures that result in numerical schemes with diverse wide-band behavior are proposed. First, an algorithm that performs better than the standard counterpart over all frequencies is constructed by requiring the mutual cancellation of terms with equal order in the corresponding dispersion relation. In addition, a second method is derived, which is founded on the separate optimization of the spatial and temporal derivatives. In this case, analysis proves that significant error compensation is accomplished around a specific design frequency, while reduced errors are obtained for higher frequencies, thus enabling the reliable execution of wide-band simulations as well. The quality and efficiency of the proposed techniques, which exhibit the same computational requirements as the standard (2,4) approach, are investigated theoretically, and subsequently, validated by means of numerical experimentation.