Taking the second derivative

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Hans123
Hans123 2019-2-7
评论： David Kohlisa 2021-3-2
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.

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Torsten
Torsten 2019-2-7
编辑：Torsten 2019-2-8
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))
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Torsten
Torsten 2019-2-11
编辑：Torsten 2019-2-11
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
David Kohlisa 2021-3-2
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.

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