The following discretization is a first order finite difference scheme
for convex speed functions [87]. This and the
scheme in Section 13.5.2 converge to the
correct viscosity solution [26,88].
are the grid values of the level set function
at
time step
and
are the values of the speed function.
Here
is written shortly for
,
which is the forward difference in
direction. The explicit values
for the next time step are
Clemens Heitzinger 2003-05-08