```Date: Jan 28, 2013 2:24 AM
Author: Bob Hanlon
Subject: Re: Help. Fitting 2 dimensional lists with a parametric differential

data1211 = {   {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}};tmax = Max[data1211[[All, 1]]];Clear[model];model[a_?NumericQ, b_?NumericQ] := y /. NDSolve[{     y'[t] == -a y[t]^2 + b (1 - y[t]),     y[0] == 0}, y, {t, 0, tmax}][[1]]Column[{   param = FindFit[data1211,     model[a, b][t], {a, b}, t],   Plot[    Evaluate[model[a, b][t] /. param],    {t, 0, tmax},    ImageSize -> 350,    PlotRange -> All,    AxesLabel -> {"t (sec)", "Ca,mol/liter"},    BaseStyle -> {FontSize -> 15},    Epilog -> {Point[data1211]}]}] // QuietBob HanlonOn Sat, Jan 26, 2013 at 1:39 AM,  <dinodeblasio@gmail.com> wrote:> 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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