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Finite Difference Approximation (FDA)

$\displaystyle {\dot y}(t,x)\approx \frac{y(t,x)-y(t-T,x)}{T}
$

and

$\displaystyle y'(t,x)\approx \frac{y(t,x)-y(t,x-X)}{X}
$

Zero-phase second-order difference:

$\displaystyle {\ddot y}(t,x) \approx \frac{y(t+T,x) - 2 y(t,x) + y(t-T,x) }{T^2}
$

$\displaystyle y''(t,x) \approx \frac{y(t,x+X) - 2 y(t,x) + y(t,x-X) }{X^2}
$



Subsections
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``Distributed Modeling in Discrete Time'', by Julius O. Smith III and Nelson Lee,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Julius O. Smith III and Nelson Lee
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA