solve ODE using mass matrix and optimize( or sfit) for constant k

Question

Abhishek Shahi 2021-5-6

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/823230-solve-ode-using-mass-matrix-and-optimize-or-sfit-for-constant-k

I have following ODE (can be up to 50 equations) and I know the inditial conditions. I would like to solve the ODEs using mass matrix approach and fit (or optimize) it for the constant k , simultaneously.

% folowing 6 ODE   
   dy1= -k(1)*y(1)
   dy2= -k(1)*y(2) + k(2)*y(3)
   dy3= -k(2)*y(3)+ k(3)*y(4)
   dy4= -k(3)*y(4) + k(4)*y(5)   
   dy5= -k(4)*y(5) + k(5)*y(6)
   dy6= -k(5)*y(6) 
  
   yo=[1:6];  % e.g. inital condition
   t=[1:11]; % time span 
   % y is the solution should be used for fitting (or optimisation )
   y=[0.0507028494426047	0.0391772076592548	0.0239936934256099	0.0136320134992300	0.00834432867659483	0.00496713242934561	0.00289990776880902	0.00227072723841650	0.00134219884538243	0.00144485869761514	0.000954842993410321
0.0449696949945177	0.0306503331602409	0.0166143496301845	0.00843215675170465	0.00470145257948545	0.00256569627280364	0.00137010277822527	0.00103256893122316	0.000561318403514916	0.000615978094736525	0.000379910700400407
0.0391124886980205	0.0233551513099763	0.0111309727505778	0.00501552652693363	0.00253435840314969	0.00126196768029146	0.000613422886429227	0.000444025306296506	0.000220983300037256	0.000247466678883997	0.000141909740882417
0.0333986566211517	0.0173566786561615	0.00722629225046896	0.00287365853628619	0.00130948595294191	0.000592232245482717	0.000260807030009474	0.000180954826980453	8.20843481602059e-05	9.38988749971876e-05	4.98825894663671e-05
0.0280293764773304	0.0125957834222410	0.00455251874259976	0.00158851929625593	0.000649668649977560	0.000265678988505308	0.000105514529162416	7.00347502676200e-05	2.88320883066407e-05	3.37246378721650e-05	1.65382627591214e-05
0.0231408090337721	0.00893630956704687	0.00278695045402996	0.000848510074328506	0.000310010718055328	0.000114140973574678	4.07005962733033e-05	2.57945112215959e-05	9.59745622162058e-06	1.14898166389124e-05	5.18346441972883e-06];
     y0=y(:,1) ;   % e.g. inital condition