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How to solve a differential equation using data from experiment?

Asked by Faezeh Manesh on 17 Sep 2019
Latest activity Commented on by Faezeh Manesh on 17 Sep 2019
Hello everyone,
Actually, I have a differential equation with the following format: Capture.PNG where Capture1.PNG .
On the other hand, I have some experimental data for dN/dT for different T . I would like to obtain N(T). Is it possible to do so with the above equation and the experimental data?

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1 Answer

Answer by Star Strider
on 17 Sep 2019

Since you are not integrating the differential equation, this is a simple nonilinear parameter estimation problem.
Try this:
T = 270:280; % Create ‘T’
dNdT = rand(size(T)); % Create ‘dNdt’
a = 42; % Create ‘a’
deltaE = 3; % Create ‘deltaE’
R = 8.3145;
objfcn = @(b,T) a.*exp(-deltaE./(R*T)) .* (1 - b); % Objective Function
B = fminsearch(@(b) norm(dNdT - objfcn(b,T)), 10); % Estimate Parameter
It might be possible to solve it as a linear problem, however that is not obvious to me just now.
Experiment to get the result you want.

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My pleasure.
Please provide the complete equation (or system of equations), including . It is likely possible to estimmte its parameters if I have a version of it I can code. (It would have been very helpful to have had all that information at the outset.)
Sure
Capture.PNG
Capture1.PNG
Capture2.PNGin concolusion the overal equation would be as follows:
Capture3.PNG
Actually, what I have from my experiments is Capture4.PNGwhith respect to T (which is about 300 data points). In addition I have a, R and delta E which are my constants, and I need delta h (which is a constant) and N(T) for different T that I have. What I am trying to do is to find N(T) and delta h through curve fitting. Could you please help me with this problem?
I forgot to tell you that I have another set of experimental data which are F with respect to T. and I have also the following equation:
Capture5.PNG
So I have N(T) in this equation too. and I am trying to find alpha (A constant) and N(T).

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