- ... time
^{2}
- , for instance, satisfies (1).
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- ... equation
^{2}
- Regrettably, a full discussion of consistency of difference schemes would take us too far afield, and we refer to [8] for a full exposition. The idea, grossly speaking, is that for a stable difference scheme, consistency is our guarantee that the numerical solution to the difference scheme converges to the solution of the continuous model problem as the grid spacing and time step are decreased. It is usually checked via a Taylor expansion of the difference scheme.
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- ... frequencies
^{2}
- As an example of such
growth at the spatial DC frequency, consider initializing the scheme
(14) using
for even and
for odd. Then we will have
, for even. It is simple to show that a waveguide
implementation does not allow us to choose bounded wave variable
initial conditions which yield these values for
and
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- ... open
^{2}
- We consider this to be the single most important issue raised in this thesis.
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