How to solve a differential equation using data from experiment?

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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?

Answers (1)

Star Strider
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.
  4 Comments
Faezeh Manesh
Faezeh Manesh on 17 Sep 2019
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?
Faezeh Manesh
Faezeh Manesh on 17 Sep 2019
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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