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March 17th, 2017, 02:17 AM   #1
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Help with equation with an unknown itegration variable

I have the following equation of the SFDM (single fracture dispersion model):



I need to fit this equation to my time (t) and concentration (y) data.
where t0, Q and M are known, and the integral is over time t. a and Pe are the fitting parameters and the integration variable is S.

I'm trying to solve this equation with MATLAB however - I am not sure where do I get S - the integration variable - from.
MATLAB keeps telling me it is an undefined variable.

How do I solve this kind of equation with an unknown integration variable?

Thanks!

Last edited by skipjack; March 17th, 2017 at 01:06 PM.
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March 17th, 2017, 01:40 PM   #2
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what is $y$ ?

might that correspond to $s$ ?
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March 17th, 2017, 06:29 PM   #3
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ok looking at this $s$ is just a dummy variable for the integral.

If this integral had a closed form you wouldn't have to deal with $s$ at all but it doesn't appear to and thus you're going to have to evaluate it numerically.

In this case you'll obtain values of $s$ by partitioning the interval $[0,t]$ in some fashion according to the numerical integration algorithm you are using.

What data do you have exactly? Do you have time samples of $c_f(t)$ ?
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