Numerics

Numerical Differentiation Formulas

1st Derivative, 5 point stencil[3]:

$f'(x) \approx \frac{-f(x+2 h)+8 f(x+h)-8 f(x-h)+f(x-2h)}{12 h}$

2nd Derivative, 5 point rule[1]

Mixed Derivative Formula[2]

[2] Numerical Recipes in C

[3] Wikipedia. "Five Point Stencil." http://en.wikipedia.org/wiki/Five-point_stencil

[4] http://www.holoborodko.com/pavel/numerical-methods/

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