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Help. Fitting 2 dimensional lists with a parametric differential

  • To: mathgroup at smc.vnet.net
  • Subject: [mg129581] Help. Fitting 2 dimensional lists with a parametric differential
  • From: dinodeblasio at gmail.com
  • Date: Sat, 26 Jan 2013 01:39:35 -0500 (EST)
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Hello everyone,
I have the following code:

Clear[y];
Column[{model = 
    DSolve[{y'[t] == -A (y[t])^2 + B (1 - y[t]), y[0] == 0}, y[t], 
      t][[1]], param = FindFit[data1211, y[t] /. model, {A, B}, t], 
   Plot[y[t] /. model /. param, {t, 0, Max[data1211[[All, 1]]]}, 
    PlotRange -> All, ImageSize -> 350, PlotStyle -> {Black}, 
    AxesLabel -> {"", "Ca,mol/liter"}, BaseStyle -> {FontSize -> 15}, 
    Epilog -> {Text["Step [1]", {50, 0.00002}], 
      Text["(sec)", {140, 0.00002}], Point[data1211]}]}] // Quiet

where "data1211" is a list as follows:
{{0., 0.}, {1., 3.26437*10^-6}, {2., 8.2151*10^-6}, {3., 
  0.0000145337}, {4., 0.000019431}, {5., 0.0000251649}, {6., 
  0.0000305308}, {7., 0.000035411}, {8., 0.0000401542}, {9., 
  0.0000449553}, {10., 0.0000499532}, {11., 0.0000545809}, {12., 
  0.0000592216}, {13., 0.0000640473}, {14., 0.0000690212}, {15., 
  0.0000740661}, {16., 0.0000782586}, {17., 0.0000822824}, {18., 
  0.0000861226}, {19., 0.0000898602}, {20., 0.0000937152}, {21., 
  0.0000978347}, {22., 0.000101408}, {23., 0.000105147}, {24., 
  0.000108497}, {25., 0.000111885}, {26., 0.000115624}, {27., 
  0.000119227}, {28., 0.000122341}, {29., 0.00012508}, {30., 
  0.000127729}, {31., 0.000130467}, {32., 0.000133645}, {33., 
  0.000136591}, {34., 0.000139623}, {35., 0.00014186}, {36., 
  0.000144227}, {37., 0.000146746}, {38., 0.000148986}, {39., 
  0.00015123}, {40., 0.000153402}, {41., 0.000155531}, {42., 
  0.0001574}, {43., 0.000159421}, {44., 0.000161271}, {45., 
  0.000162982}, {46., 0.000164705}, {47., 0.000166305}, {48., 
  0.000167756}}

Now I'd like to fit the equation: y'[t] == -A (y[t])^3 + B (1 - y[t]),
by using NDsolve and find the two parameters A and B.

Can anyone help on this?
Thank really much for your help.
Dino 



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