  Backwards-wave (BW) materials that have simultaneously negative real parts of
their electric permittivity and magnetic permeability can support waves where
phase and power propagation occur in opposite directions. These materials were
predicted to have many unusual electromagnetic properties, among them
amplification of the near-field of a point source, which could lead to the
perfect reconstruction of the source field in an image [J. Pendry, Phys. Rev.
Lett. \textbf{85}, 3966 (2000)]. Often systems containing BW materials are
simulated using the finite-difference time-domain technique. We show that this
technique suffers from a numerical artifact due to its staggered grid that
makes its use in simulations involving BW materials problematic. The
pseudospectral time-domain technique, on the other hand, uses a collocated grid
and is free of this artifact.
  It is also shown that when modeling the dispersive BW material, the linear
frequency approximation method introduces error that affects the frequency of
vanishing reflection, while the auxiliary differential equation, the Z
transform, and the bilinear frequency approximation method produce vanishing
reflection at the correct frequency. The case of vanishing reflection is of
particular interest for field reconstruction in imaging applications.
