Solve a system of differential equations with experimental values of one depedent variable.

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Johan Sebastian Diaz Tovar 2019-8-2

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https://ww2.mathworks.cn/matlabcentral/answers/474663-solve-a-system-of-differential-equations-with-experimental-values-of-one-depedent-variable

评论： Star Strider 2019-8-3

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Hello, everybody.

I'm trying to solve this system of differential equations:

and basicaly what I want to do is have a numerically solution of the function

introducing experimental data of

, for that i used this code where i can solve the problem and fit the curves to finally have the values that I want

(theta(1)) and

(theta(2)):

function test01
L = 808e-9;    %m. Wavelength
hc= 1.986e-25; %W.s.m Planck constant * speed of light.
I = 116e-3;    %W/cm^2 initial intensity
function C=kinetics(theta,t)
c0=[0.96437;0];
[T,Cv]=ode45(@DifEq,t,c0);
%
    function dC=DifEq(t,c)
    dcdt=zeros(2,1);
    dcdt(1)= -L*I*theta(1).*(1-theta(2)).*c(1);  
    dcdt(2)= L*I*theta(1).*theta(2).*c(1); 
    dC=dcdt;
    end
C=Cv;
end
t=[0 
66 
132 
198 
264 
330 
396 
462 
528 
594 
660];
c=[0.96437	0.061
0.81894	0.1128	
0.71044	0.1568	
0.63977	0.1942	
0.53643	0.2259	
0.46207	0.2529	
0.39372	0.2736	
0.33552	0.2934	
0.2854	0.3101	
0.24209	0.3243	
0.213	0.3358];
err=[0.04622    0.001
0.03544 0.001
0.02994 0.002
0.03702 0.002
0.01933 0.001
0.02637 0.001
0.03497 0.001
0.0163  0.002
0.02451 0.002
0.0064  0.001
0.01229 0.001];
theta0=[1,1];
[theta,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat]=lsqcurvefit(@kinetics,theta0,t,c);
fprintf(1,'\tRate Constants:\n')
for k1 = 1:length(theta)
    fprintf(1, '\t\tTheta(%d) = %8.5f\n', k1, theta(k1))
end
tv = linspace(min(t), max(t));
Cfit = kinetics(theta, tv);
figure(1)
errorbar(t, c(1:11), err(1:11), 'p')
hold on
errorbar(t, c(12:22), err(12:22), 'p')
hold on
hlp = plot(tv, Cfit);
hold off
grid
xlim([-25 700])
ylim([0 1.05])
xlabel('Time')
ylabel('Concentration')
legend(hlp, 'C_1(t)', 'C_2(t)', 'Location','N')
end

but, to have the problem solved, I had to force and put fake values of

. For that, I would like to have any suggestion for this problem, I would like to solve the problem introducing the experimental data I have, and have a curve solution of

and the best fitting for this two to have the values:

and

For other hand, if you guys can give me an idea for solving a system of differential equations in matlab when that system has two independent variables, like this case:

Thank you so much for your value help!!!!

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Star Strider 2019-8-3

Your system of differential equations are functions of

only, not D, so the ‘kinetics’ function is not integrating D but something else that is not explained or described (although it appears to be tangentially related to