Finite Difference Approximation

A finite difference approximation (FDA) approximates derivatives with finite differences, i.e.,

$$\frac{d}{dt} x(t) \isdefs \lim_{\delta\to 0} \frac{x(t) - x(t-\delta)}{\delta} \;\approx\; \frac{x(n T)-x[(n-1)T]}{T} \protect$$ (8.2)

for sufficiently small $T$ .^8.5

Equation (7.2) is also known as the backward difference approximation of differentiation.

See §C.2.1 for a discussion of using the FDA to model ideal vibrating strings.