How to solve a differential equation using data from experiment?

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?

Answer 1

[Star Strider]

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.

[Faezeh Manesh]

Thanks for your help. Actually N is also a function of T which means that it varies with different T and I need N for each T. Is it possible to do it in a way that I can find N for each T?

[Star Strider]

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]

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]

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).