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HK
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Solving Multiple First Order Differential Equations for Constants

Asked by HK
on 15 Feb 2019
Latest activity Commented on by Torsten
on 20 Feb 2019
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Hi,
I hope someone can help me.
I am looking to solve these 6 first order differential equations for the unknowns k1, k2, k3, k4, k5 and k6, with known concentrations in the square brackets (any number for them will do just now to get a working script!). Could someone help me obtain a script to do this?
Many thanks in advance.

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1 Answers

Answer by Torsten
on 15 Feb 2019
 Accepted Answer

Replace the time derivatives by difference quotients.
Then you get a linear system of equations
A*[k1;k2;k3;k4;k5;k6] = b
where the number of rows in A is equal to (6*number of measurement times).
This can subsequently be solved using
k = A\b.
Best wishes
Torsten.

  8 Comments

To get approximate values for k1,...,k6, you need measurement data for the concentrations [TG], [DG],,...,[MeOH] at different times t1,...,tn, not only at t=0. Do you have such data ?
Yes, I have concentration data at the end of the reaction (t=60 mins/3600s) and also at two intermediate times (t = 2 mins/120s and t = 12 mins/720s). Should I state all of these values at the top of the script like I did for the values at t=0? Should the script then run or do additional changes need to be made in its layout?
Thanks again!
Since your data are taken at times with such a great temporal distance, you should try the method described here:
Best wishes
Torsten.

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