Parameter Estimates for Ordinary Differential Equation

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I am seeking very simply to estimate the paramter c1 in the following ordinary differential equation:
dT/dt = c1*T*( 1 if t > 0, 0 if t = 0) - 0.33*T
by fitting this equation to the following set of data through minimizing differences between numerical output and data values:
t=[0, 2, 7, 12]
T=[18.8479, 18.2949, 68.2027, 32.5346]
Thank you for any help.

Accepted Answer

Bjorn Gustavsson
Bjorn Gustavsson on 27 May 2022
Solve the ODE analytically. That will give you an expression for T(t,c1) this you can then use for a standart non-linear least-square-fit to your data (), using for example fminsearch or lsqnonlin.
HTH

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