
Problems with fitting a first order differential equation
Posted:
Dec 2, 2011 6:36 AM


Dear all,
I have a list of values (2dimensional). 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 twodimensional by using the models above?
Thanks. Dino

