Solving Multiple First Order Differential Equations for Constants
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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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Torsten
2019-2-15
1 个投票
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 个评论
HK
2019-2-15
Torsten
2019-2-18
Which data from measurements do you have ?
HK
2019-2-18
Torsten
2019-2-18
Ok. Then for [TG], e.g., you can use the equations
[TG]_(i+1) - [TG]_(i) = dt * (-k1*[TG]_(i+1)*[MeOH]_(i+1) + k2*[DG]_(i+1)*[ME]_(i+1))
for i=1,2,...,N.
Same for the other components.
You see that you get a linear system of equations in the unknowns k1,k2,...,k6, as stated above.
This can be solved using the mldivide - operator.
HK
2019-2-18
Slowly but surely I think I am getting somewhere! (Sorry I am inexperienced with Matlab and trying to improve).
Can you identify the errors that I still have? Am I solving for k in the command window correctly? All of the equations for 'TG(i+1) - TG(i)' etc are in correctly but there are errors around the equals signs saying 'Parse error at '=': usage might be invalid MATLAB syntax'.
HK
2019-2-20
Torsten
2019-2-20
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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