 ADI- boundary. [Cost03] therefore has studied Liao's second FDTD to such dispersive environments is required to order boundary condition with an emphasis on obtaining accommodate UWB systems. Holloway et al. a reduced memory requirement and improved stability. [SHBPM03], [HMDA02] accounted for material dis- The results of this work can, however, be applied to persion in the magnetic field and mentioned the possi- higher order Liao's AbBCs. The detail of the numerical bility of dealing with material dispersion in the electric formulation is given in [Cost03]. This novel AbBC re- field. However, [SHBPM03] and [HMDA02] do not give duces the data storage requirement for the boundary an implementation of ADI-FDTD which deals with calculation of the original AbBC by 33%. [WaCh95] material with FD permittivity E and ohmic losses. Yuan pointed out that the high stability is realised when the and Chen's [YuCh03] concern focuses on conductive poles of the artificial reflection coefficient are within the materials. Garcia et al. [GRBM03] deal with the Debye unit circle of the complex plane. Based on this, the pos- model utilising the electrical polarisation vector field. sible instability caused by the proposed boundary con- The COST 273 project [Cost04], [ThCo04], [CoTh04a], dition is investigated, compared with the original 2nd proposes an alternative technique using the electric flux order Liao AbBC. The study showed another merit of the density D, similar to the work by Schmidt and Lazzi proposed AbBC, that is, the proposed AbBC gains its [ScLa03], but with FD materials for UWB systems. This stability with a < 0.5 while the original AbBC has in- runs parallel to [GRBM03] and provides convergent ev- stability with any a. The reflection coefficient from the idence for the general approach to FD materials in ADI- proposed AbBC in the time domain was calculated with FDTD class problems. The novelty of this work is in the marginally stable damping parameter a = 0.5, com- proposing an FD-ADI-FDTD which can deal with Debye pa