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March 17th, 2017, 03:17 AM  #1 
Newbie Joined: Mar 2017 From: Israel Posts: 1 Thanks: 0  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 02:06 PM. 
March 17th, 2017, 02:40 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816 
what is $y$ ? might that correspond to $s$ ? 
March 17th, 2017, 07:29 PM  #3 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816 
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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