# Taylor series

$f_{i+1}=f_i+hf'_i+\frac{h^2}{2!}f''_i+\frac{h^3}{3!}f'''_i+...$
$f_{i-1}=f_i-hf'_i+\frac{h^2}{2!}f''_i-\frac{h^3}{3!}f'''_i+...$