What could be a faster way to calculate first derivative of a field?

I want to calculate first derivative (using second-order FDM) of a 1D field that is quite large, about 12 million points. Instead of using:

for i = 2:(N-1)
    dfdt(i) = (f(i+1)-f(i-1))/(2*dt);
end

can I do something else which takes advantage of some innate feature of MATLAB that could potentially reduce the total computational time?

Answer 1

[Bruno Luong]

dfdt = (f(3:end)-f(1:end-2))*(1/(2*dt))