Problems with fitting a first order differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg123336] Problems with fitting a first order differential equation
- From: Dino <dinodeblasio at gmail.com>
- Date: Fri, 2 Dec 2011 07:20:18 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
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