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Topic: Problems with fitting a first order differential equation
Replies: 0

 dinodeblasio@gmail.com Posts: 23 Registered: 10/14/07
Problems with fitting a first order differential equation
Posted: Dec 2, 2011 6:36 AM

Dear all,

I have a list of values (2-dimensional). data={{xi,yi}...}
And I finally am able to fit them as the example below:
and find the parameters A and B
-----------------------------------
Clear[y];
data = {{1, 0.033}, {2, 0.054}, {5, 0.088}};
With[{C = 1/9},
Column[{
model = DSolve[
{y'[t] == -A (y[t])^2 + B (C - y[t]), y[0] == 0},
y[t], t][[1]],
param = FindFit[data, y[t] /. model, {A, B}, t],
Plot[y[t] /. model /. param, {t, 0, Max[data[[All, 1]]]},
ImageSize -> 400, AxesLabel -> {"t", "y[t]"},
Epilog -> {Red, AbsolutePointSize[5], Point[data]}]}]] // Quiet
---------------------------
Thanks to Bob Hanlon.

However I would like to fit the same data by using different exponents
of the term y[t])^2 which appear on the right hand side of the
differential equation:
for example I'd like to use:

{y'[t] == -A (y[t])^3 + B (C - y[t]), y[0] == 0},
or
{y'[t] == -A (y[t])^(2.5) + B (C - y[t]), y[0] == 0},

Is that anyway to fit a list of two-dimensional by using the models
above?

Thanks.
Dino