*Finite Difference Schemes* (FDSs) aim to solve differential
equations by means of finite differences. For example, as discussed
in §G.2, if denotes the displacement in meters of a vibrating
string at time seconds and position meters, we may approximate
the first- and second-order partial derivatives by

where denotes the time sampling interval and denotes the spatial sampling interval. These finite-difference approximations to the partial derivatives may be used to compute solutions of differential equations on a discrete grid:

where is a positive real constant (which turns out to be wave propagation speed). Then, as derived in §G.2, setting and substituting the finite-difference approximations into the ideal wave equation leads to the relation

The FDS is called

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