Taking the second derivative

I have two arrays M and V, both are the same dimesions.

I am trying to find and plot this vs. M, this is the code I am working with - but it doesn't work - what should I do?

second_der = diff(V_preamp,2)./diff(M,2);

The probem with the above code is it creates a second derivative code that is shorter than the independent variable I am plotting the graph with (independent variable - M)

How can I fix this isse.

Answer 1

[Torsten]

second_der = zeros(size(V_preamp));
second_der(2:end-1) = ((V_preamp(3:end)-V_preamp(2:end-1))./...
                       (M(3:end)-M(2:end-1))-...
                       (V_preamp(2:end-1)-V_preamp(1:end-2))./...
                       (M(2:end-1)-M(1:end-2)))./...
                       (0.5*(M(3:end)-M(1:end-2)));
plot(M(2:end-1),second_der(2:end-1))

[Hans123]

Hi Torsten,

Thanks for that answer! I get a matrix dimensions don't agree error.

Can you tell me how you got the second derivative?

[Torsten]

Code corrected.

Best wishes

Torsten.

[Hans123]

Thanks a lot, it works - If I may ask, how did you get the equation to find the second derivative?

[Torsten]

It's the usual finite difference approximation for the second derivative.

On uniform grids,

f''(x_i) = (approximately) (f(x_i-h)-2*f(x_i)+f(x_i+h))/h^2

On non-uniform grids

f''(x_i) = (approximately) ((f(x_(i+1)-f(x_i)))/(x_(i+1)-x_i) - (f(x_i)-f(x_(i-1)))/(x_i-x_(i-1)))/(0.5*(x_(i+1)-x_(i-1)))

[David Kohlisa]

For the two arrays V and M you have, V must be equal to some function of M where V = f(M).

To get the second derivative of V with respect to M it is simply:

d2VdM2 = diff(V, M, 2)

where V=f(M), M is what you differentiating with respect to and 2 is order of the derivative.