Time-Space Grid of Second-Order FDS

$$\begin{eqnarray*} u_{k}^{n+1} = u_{k-1}^{n}+u_{k+1}^{n}-u_{k}^{n-1} \end{eqnarray*}$$

Grid variable at ``current'' point depends on value at two previous time steps (a second order scheme in time). We thus need to specify initial data for all $m$ at times $n=0$ and $n=1$ .

Grid variable at ``current'' point depends on values at adjacent locations on the string (at previous time).

Difference scheme is explicit (thus parallelizable); that is, each grid variable at time $n+1$ depends only on grid variables at previous time instants. This is a very desirable property.