Fórmulas Diferenciación Numérica

Fórmulas Primeras Derivada

Siempre tener en cuenta que $h = x_{i + 1} - x_{i}$

$f^{'} (x_{i}) \approx \frac{f ( x _{i + 1} ) - f ( x _{i} )}{h}$

$f^{'} (x_{i}) \approx \frac{- f ( x _{i + 2} ) + 4 f ( x _{i + 1} ) - 3 f ( x _{i} )}{2 h}$

$f^{'} (x_{i}) \approx \frac{f ( x _{i} ) - f ( x _{i - 1} )}{h}$

$f^{'} (x_{i}) \approx \frac{3 f ( x _{i} ) - 4 f ( x _{i - 1} ) + f ( x _{i - 2} )}{2 h}$

Diferenciación centrada

$f^{'} (x_{i}) \approx \frac{f ( x _{i + 1} ) - f ( x _{i - 1} )}{2 h}$

$f^{'} (x_{i}) \approx \frac{- f ( x _{i + 2} ) + 8 f ( x _{i + 1} ) - 8 f ( x _{i - 1} ) + f ( x _{i - 2} )}{12 h}$

Diferenciación hacia adelante

$f^{''} (x_{i}) \approx \frac{f ( x _{i + 2} ) - 2 f ( x _{i + 1} ) + f ( x _{i} )}{h ^{2}}$

$f^{''} (x_{i}) \approx \frac{- f ( x _{i + 3} ) + 4 f ( x _{i + 2} ) - 5 f ( x _{i + 1} ) + 2 f ( x _{i} )}{h ^{2}}$

Diferenciación hacia atrás

$f^{''} (x_{i}) \approx \frac{f ( x _{i} ) - 2 f ( x _{i - 1} ) + f ( x _{i - 2} )}{h ^{2}}$

$f^{''} (x_{i}) \approx \frac{2 f ( x _{i} ) - 5 f ( x _{i - 1} ) + 4 f ( x _{i - 2} ) - f ( x _{i - 3} )}{h ^{2}}$

Diferenciación centrada

$f^{''} (x_{i}) \approx \frac{f ( x _{i + 1} ) - 2 f ( x _{i} ) + f ( x _{i - 1} )}{h ^{2}}$

$f^{''} (x_{i}) \approx \frac{- f ( x _{i + 2} ) + 16 f ( x _{i + 1} ) - 30 f ( x _{i} ) + 16 f ( x _{i - 1} ) - f ( x _{i - 2} )}{12 h ^{2}}$