Time-Space Grid for the Second-Order Ideal String FDS

$$\begin{eqnarray*} y_{m}^{n+1} = y_{m-1}^{n}+y_{m+1}^{n}-y_{m}^{n-1} \end{eqnarray*}$$

• Grid variable at ``current'' point depends on value at two previous time steps (a second order scheme in time). Our initial conditions must therefore specify $y(n,m)$ 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.