Convolution integral equation ode15s

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Davide Masiello
Davide Masiello 2019-3-13
评论： Torsten 2019-3-13
I am solving a DAE system in Matlab using the ode15s suite. I'd like to add a further equation that I found in literature which reads:
R and F are two of the functions I am already integrating in the system and they are both dependent on the time t only, while x and y should be dummy integration variables.
I can't numerically calculate the integrals because it would need all the previos values of R and F in time, to which I have not access from within the function.
I also don't know how to correctly perform a time derivative of such a kind of equation.
If anyone has faced this problem already, it would be great to have som feedback from him/her. Thanks.
P.S.: since I am not familiar with this problem at all, please feel free to suggest more appropriate question's title and tags.
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Davide Masiello
Davide Masiello 2019-3-13
Hi Torsten.
Since x is the integration variable of the outer integral I assumed that, for any time t, x spans from 0 to t. I am not totally sure of this, but it is also the only option that makes sense to me. In all the references I found, both x and y appear only within those integrals (i.e. they are not defined anywhere else in the system) and therefore I don't think they have any physical meaning.
Torsten
Torsten 2019-3-13
I don't think that it is possible to write an ODE for T_li(t) that can be solved simultaneously with the ones for R and F.
You should calculate T_li(t) with the discrete data for R and F after integration using "interp1" for interpolation and "integral".

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