MATLAB: ODE and Data fitting

curve fittingMATLABode45

I have 3 differential equations:

The initial condition for all the equations at timepoint=0 equal to 0. After solving this equaitons, I want to a data fitting on the equation below in order to find the nest fitted A, B, and C.

Can someone help me on this, because I face several errors when I tried to do it.

Maybe the best way is to find the u, v, and w functions and then place them in equations x and y; but how can I do it? is there any way that ode45 give the formula of u,v, and w?

Best Answer

All I can do is to point you in the direction of successful efforts to do what you want.

One such is: Parameter Estimation for a System of Differential Equations and another is of course Monod kinetics and curve fitting.

We can’t help without seeing your code.

Related Solutions

MATLAB: Error occurs in the present code

You have a typographical error in your odeset call. You typed ‘l’ (lower-case ‘L’) instead of the number 1.

Use this instead:

options=odeset('RelTol',1e-8,'AbsTol',1e-8);

and your code runs without error.

When I ran it,, the result was:

x1 =
     3.732

MATLAB: Parameter estimation and curve fitting

Dear Star Strider,
thank you for your response. Unfortunatelly, I haven't solve my problem yet. I applied your scripts, as you advised me. At first, they responsed but the results weren't logical. After some runs (playing with the initial conditions) there were no results. And now there is this message:
Error using lsqcurvefit (line 248)
Function value and YDATA sizes are not equal.
Error in MonodKinetics1_test (line 11)
[v,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(@MonodKinetics1,v0,tdata,Ydata);
The scripts are the following:
The function:
function Y = MonodKinetics1(v, t)
y0 = rand(4,1)*1000;
[T,Yv] = ode45(@DifEq, t, y0);
      function dS = DifEq(t, y)
         dy=zeros(4,1);
          N=y(1)+y(2)+y(3)+y(4);
          dy(1)=-v(1)*y(1)*y(3)/N-v(2)*y(1);
          dy(2)=v(1)*y(1)*y(3)/N-v(3)*y(2)-v(4)*y(2)*y(3)/N-v(5)*y(2);
          dy(3)=v(2)*y(1)+v(3)*y(2)+v(4)*y(2)*y(3)/N-v(6)*y(3);
          dy(4)=v(5)*y(2)+v(6)*y(3);
          dS = dy;
        end
  Y = Yv(:,1);
  end
and I run script:
load R_data.dat  % loading data
 format long
 tdata=R_data(:,1);
 Ydata=R_data(:,2:5);
   v0 = rand(6,1);
  [v,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(@MonodKinetics1,v0,tdata,Ydata);
The data are described adove (first message).
Could you help me more, please? 
I apprecciate everydoby who help me to continue with my project.
Thanks

Best Answer

Related Solutions

MATLAB: Error occurs in the present code

MATLAB: Parameter estimation and curve fitting

Related Question