How to solve a differential equation using data from experiment?

Asked by Faezeh Manesh

Faezeh Manesh (view profile)

on 17 Sep 2019
Latest activity Commented on by Faezeh Manesh

Faezeh Manesh (view profile)

on 17 Sep 2019
Hello everyone,
Actually, I have a differential equation with the following format: where .
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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Answer by Star Strider

Star Strider (view profile)

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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Star Strider

Star Strider (view profile)

on 17 Sep 2019
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.)
Faezeh Manesh

Faezeh Manesh (view profile)

on 17 Sep 2019
Sure   in concolusion the overal equation would be as follows: Actually, what I have from my experiments is whith 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 (view profile)

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: So I have N(T) in this equation too. and I am trying to find alpha (A constant) and N(T).