Taking derivative an array which is a numerical value with respect to another array
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Roger Stafford on 3 May 2015
Edited: Roger Stafford on 3 May 2015
Here is a second order approximation to du/dx which should be somewhat more accurate than a first order approximation, and if u is a quadratic function of x, then du/dx is exact (except of course for round-off errors.) Also note that there are as many points in the derivative array as in u and x. I assume in this code that u and x are row vectors of the same length. Intervals in x are not required to be equal.
xd = diff([x(3),x,x(n-2)]); % <-- Corrected
ud = diff([u(3),u,u(n-2)]); % <-- Corrected
dudx = (ud(1:end-1)./xd(1:end-1).*xd(2:end) ...
+ ud(2:end)./xd(2:end).*xd(1:end-1)) ...
More Answers (1)
pfb on 2 May 2015
if f is the vector representing f(x) and x contains the corresponding abscissae
df = diff(f)./diff(x)
note that this has one less element than f and x. You can choose
xd = (x(1:end-1)+x(2:end))/2
(i.e. the halfway points) as the corresponding abscissae.