How do I integrate the output of an ode23 solver?

In my specific problem I have solved an ODE with ode23 resulting in two 11x1 double vectors (E and r). The dr's resulitng are equal in size, in this case. The integrate function does work on these variable types, or can it? Creating a simple "for" loop multiplying E(i)*dr and summing is too course (11 points) and gives the wrong answer, which I know exactly. The plotted output of ode23 shows a solid line between the 11 points. So, some kind of extrapolation or estimated function must exist, or? That then could be integrated with the function integrate, or?

Answer 1

[Torsten]

Solve the additional ODE

dI/dt = E(t)*dr/dt

then

I(T) = integral_{t=0}^{t=T} E(t) dr

Best wishes

Torsten.

Answer 2

[Marc Jeroense]

I am afraid I do not quite understand you. I added my short trial file. Hope you can have a look? I now used the trapz function. I expected the result to be more accurate.

[Torsten]

If a quantity e is the result of a solution of an ODE

de/dt = ...

and in addition to e, you want to have the integral of e over time (name it E), you can add the differential equation

dE/dt = e, E(0)=0

to your system of ODEs.

Then

E(T) = integral_{t=0}^{t=T} e(t) dt

Best wishes

Torsten.