How to do curve fitting with differential equation?

I have a differential equation as,

dotn(1) = -k_rs*n(1)-k_ISC*n(1)-k_SS*n(1)^2-k_ST*n(1)*n(2)+0.25*k_TT*n(1)^2;

Here k_SS, k_TT and k_ST is unknown (my plan is to get them from experimental data by fitting)

I want to fit this equation into n(1) vs time graph. Please let me know your suggestions.

Answer 1

[madhan ravi]

https://www.mathworks.com/matlabcentral/answers/132238-how-to-fit-experimental-data-on-only-one-ordinary-differential-equations-out-of-multiple-equations#answer_139484

https://www.mathworks.com/matlabcentral/answers/413401-find-parameters-for-differential-equations-for-specific-data#answer_331468

[Monirul Hasan]

Hi Madhan, Please have look on my code, mathematical model and experimental data (all attached

with this comment). The output are changing with each run. Also please let me know how to plot the fit curve as well.

    %
clear all, close all,  clc
load("CBP4czEx37213us")
Time = CBP4czEx37213us.Timens;
Sdata = CBP4czEx37213us.Decay;
%plot(Time,Sdata,'bo',Time,MonodKinetics1(B,Time),'g-')
%set(gca,'yscale','log')
B0 = rand(7,1)*100;
[B,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(@MonodKinetics1,B0,Time,Sdata);
function S = MonodKinetics1(B,t)
IC_ns = 10000;
IC_nt = 0;
IC = [IC_ns IC_nt];
tspan = 0:3.5117:14383.75936;
  function dotn = Matlabform (t,n)
%       k_rs = 3.2e7; B(1)
%      k_ISC = 0.15* k_rs;  B(2)
%      k_RISC = 5.6e2; B(3)
%      k_SS = 3.5e-12; B(4)
%      k_ST = 1.9e-10; B(5)
%      k_TT = 2.2e-15; B(6)
%      k_NRT = 8.2e2; B(7)
 dotn = zeros(2,1);
     dotn(1) = -B(1)*n(1)-B(2)*n(1)+B(3)*n(2)-B(4)*n(1)^2-B(5)*n(1)*n(2)+0.25*B(6)*n(2)^2;
     dotn(2) = -B(3)*n(2)+B(2)*n(1)-B(7)*n(2)-1.25*B(6)*n(2)^2;
  end
[t,nsol] = ode15s(@Matlabform,tspan,IC);
S = nsol(:,1);
end

[Monirul Hasan]

Also thanks for the links in the 1st comment. I made this code based on link 1.