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

Question

Dursman Mchabe 2020-12-24

0
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https://ww2.mathworks.cn/matlabcentral/answers/701597-solve-a-system-of-four-differential-equations-with-experimental-values-of-one-dependent-variable

Hi everyone,

On the code below, is it posible to solve a system of four differential equations with experimental values of one dependent variable? The code runs well when I solve one ODE.

function Igor
% 2016 12 03
% NOTES: 
% 
%   1. The ‘theta’ (parameter) argument has to be first in your 
%       ‘kinetics’ funciton,
%   2. You need to return ALL the values from ‘DifEq’ since you are fitting
%       all the values
    function C=kinetics(theta,t)
    %c0=[1;0;0;0];
    c0=[1];
    [T,Cv]=ode45(@DifEq,t,c0);
%
            function dC=DifEq(t,c)
%             dcdt=zeros(4,1);
dcdt=zeros(1,1);
            dcdt(1)=-theta(1).*c(1)-theta(2).*c(1);
%             dcdt(2)= theta(1).*c(1)+theta(4).*c(3)-theta(3).*c(2)-theta(5).*c(2);
%             dcdt(3)= theta(2).*c(1)+theta(3).*c(2)-theta(4).*c(3)+theta(6).*c(4);
%             dcdt(4)= theta(5).*c(2)-theta(6).*c(4);
            dC=dcdt;
            end
    C=Cv(:,:);
    end
t=[0.1
0.2
0.4
0.6
0.8
1
1.5
2
3
4
5
6];
c=[0.902	
0.8072	
0.6757	
0.5569	
0.4297	
0.3774	
0.2149	
0.141	
0.04921	
0.0178	
0.006431	
0.002595]; 
% theta0=[1;1;1;1;1;1];
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)
plot(t, c, 'p')
hold on
hlp = plot(tv, Cfit);
hold off
grid
xlabel('Time')
ylabel('Concentration')
% legend(hlp, 'C_1(t)', 'C_2(t)', 'C_3(t)', 'C_4(t)', 'Location','N')
end