Take the 2-minute tour ×  If they say that $f_i$ is the central
difference discrete of $f(t,x)$ in the point $(t_n,x_i)$.  What
do they mean by this?  share|improve this question add comment
1 Answer  up vote 0 down vote accepted  Typically a central
difference means you compute $f(x_{i+1}) - f(x_{i-1})$ and often
you may divide by $\frac{1}{2 \Delta t}$ or something similar.
The key thing is that a difference is computed where $f(x_i)$ is
in the centre of the two things which we're subtracting.  See
http://en.wikipedia.org/wiki/Finite_difference for more
information  In your case where you have a function of two
variables, you may take $4$ points to average over. There are
equivalent notions for higher order functions.  share|improve
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