Parameter Estimates for Ordinary Differential Equation

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.

Answer 1

[Bjorn Gustavsson]

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