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## Solving Multiple First Order Differential Equations for Constants

### HK (view profile)

on 15 Feb 2019
Latest activity Commented on by Torsten

on 20 Feb 2019

### Torsten (view profile)

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?

### Torsten (view profile)

on 15 Feb 2019

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.

Torsten

### Torsten (view profile)

on 20 Feb 2019
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 ?
HK

### HK (view profile)

on 20 Feb 2019
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!
Torsten

### Torsten (view profile)

on 20 Feb 2019
Since your data are taken at times with such a great temporal distance, you should try the method described here:
Best wishes
Torsten.