How to adjust parameters in a ode?

I have an equation like this:

dy/dt = alpha * x(t)

The function x(t) is known and I have experimental data for dy/dt.

How can I find the value of alpha adjusting the equation to the experimental data?

Thank you!

Answer 1

[David Goodmanson]

Hi Sara

Since you have a single multiplicative parameter, certainly the simplest way is,

create a column vector dydt of your data

create a column vector t of corresponding experimental times

then

 prediction = x(t)           % assuming x can accept a vector and produce a vector
 alpha = prediction\dydt

This works since

alpha x(t) = dy/dt

is a set of n linear equations and one unknown, so Matlab finds a least square solution for alpha. Of course this only works if dydt and the prediction x(t) have some sensible relation to each other, i.e. basically the same shape. More sophisticated solutions are probably possible but this is worth trying first.

[Sara Jiménez]

Thank you!