# Accuracy of the first derivative with ode45

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I G il 3 Lug 2018
Commentato: I G il 4 Lug 2018
I am using ode45 to get solution of system with 4 differential equation of the first order. ode45 gives me result as value, but I need the first derivative of that value. So, I found two methods to do that.
First one, is the gradient command. The second one is sol and deval commands together. My question is, which of these two methods will give me more accurate result? And which of these two methods will give me accuracy of result same as accuracy of ode45?
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### Risposte (1)

Torsten il 3 Lug 2018
The most accurate method is to use the derivatives you set by yourself in the function routine that ODE45 calls (the dydt(i) values).
Best wishes
Torsten.
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James Tursa il 3 Lug 2018
Your derivative function is not vectorized, so you need to call it in a loop. E.g.,
dp = zeros(size(pv));
for k=1:size(pv,1)
dp(k,:) = fun(zv(k),pv(k,:));
end
I G il 4 Lug 2018
This works. Thanks a lot!

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