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I need to find the parameters (k1,k2,k3,k4,k1r,k2r,k3r,k4r) that fit my data (list of [Intensity, time]) using the function b(t), solution of the following system of parametric ODE:

{a'[t] == -k1*a[t] - k2*a[t] + k1r*g[t] + k2r*p[t],
 g'[t] == -k1r*g[t] - k3*g[t] + k1*a[t] + k3r*b[t],
 p'[t] == -k4*p[t] - k2r*p[t] + k4r*c[t] + k2*a[t],
 b'[t] == -k3r*b[t] + k3*g[t],
 c'[t] == k4*p[t] - k4r*c[t]}

Initial conditions:

a[0] == 1,
c[0] == 0,
b[0] == 0,
p[0] == 0,
g[0] == 0,

The system of ODE has no analytical solution, so I tried to use NDSolve, but it is of course not working because the ODEs are parametric. I guess ParametricNDSolve would help me, but unfortunately it is not implemented in the version of Mathematica I am using (Mathematica 8). Do you have any idea about how to address this problem, avoiding the ParametricNDSolve function?


marked as duplicate by Daniel Lichtblau, Öskå, RunnyKine, Yves Klett, bobthechemist Jul 31 '14 at 19:33

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  • 1
    $\begingroup$ See Help > Wolfram Documentation > FindFit > Applications > Differential Equations for an example. I will give several MSE links in a followup comment. $\endgroup$ – Daniel Lichtblau Jul 31 '14 at 16:35
  • $\begingroup$ Here are variants of this question, many with responses. I found them using Google and wsearching for (without the quotes) "mathematica stackexchange fit differential". 1 2 3 4 $\endgroup$ – Daniel Lichtblau Jul 31 '14 at 16:37
  • $\begingroup$ More MSE links: 5 6 7 $\endgroup$ – Daniel Lichtblau Jul 31 '14 at 16:38
  • $\begingroup$ As far I see, all these examples use ParametricNDSolve, am I right? I would need an alternative method, because I don´t have Mathematica 9. Thanks $\endgroup$ – Irene Jul 31 '14 at 20:56
  • $\begingroup$ Several of the links I gave provide responses that use NDSolve rather than ParametricNDSolve. $\endgroup$ – Daniel Lichtblau Jul 31 '14 at 22:57