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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*}

\epsfig{file=eps/1ddep.eps,width=6in}

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.


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``Discrete-Time Lumped Models'', by Stefan Bilbao and Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Stefan Bilbao and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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