Using centered finite difference approximations (FDA) for the
second-order partial derivatives, we obtain a *finite difference
scheme* for the ideal wave equation
[30,18]:

where is the time sampling interval, and is a spatial sampling interval.

Substituting the FDA into the wave equation, choosing , where is sound speed (normalized to below), and sampling at times and positions , we obtain the following explicit finite difference scheme for the string displacement:

where the sampling intervals and have been normalized to 1. To initialize the recursion at time , past values are needed for all (all points along the string) at time instants and . Then the string position may be computed for all by Eq. (4) for . This has been called the

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