Grid Functions

A grid function $u_{l}^{n}$, taking on values for integer $n\geq 0$, and for integer $l\in{\mathbb{Z}}$, is introduced in order to approximate a continuous function $u(x,t)$, at location $x=lh$, and at time $t=nk$. Again, as in the case of time series, the same variable name (in this case $u$) will be used to represent both a grid function, and the variable it is intended to approximate. For the moment, for simplicity, it will be assumed that grid functions are infinite in spatial extent, though the bounding of spatial domains will be introduced in §5.1.8.