Abstract
This paper examines the most popular advances in the FDTD algorithm development, as applied to electromagnetic wave propagation in linearly dispersive media. Several methodologies are presented, and comparisons are made in order to demonstrate the strengths and weaknesses of the various approaches. In particular, direct-integration and recursive-convolution schemes, associated with wave propagation in a cold plasma, Debye dielectrics, and Lorentz materials, are considered.

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