Finite Difference Time Domain (FDTD) Scheme
As discussed in §C.2, we may use centered finite
difference approximations (FDA) for the
second-order partial derivatives in the wave equation to obtain a
finite difference scheme for numerically integrating the ideal
wave equation [481,311]:
where


Substituting the FDA into the wave equation, choosing ,
where
is sound speed (normalized to
below), and sampling at times
and positions
, we
obtain the following explicit finite difference scheme for the string
displacement:
where the sampling intervals









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Digital Waveguide (DW) Scheme
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Convergence in Audio Applications