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MathGroup Archive 2007

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NDSolve, Loop, Table, Plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77583] NDSolve, Loop, Table, Plot
  • From: Solver <shawnleroux at hotmail.com>
  • Date: Wed, 13 Jun 2007 07:35:30 -0400 (EDT)

Hi,

I have a system of 3 differential equations and I would like to
numerically solve them for different values of one parameter (e.g., p1
= 0.5, 0.6, 0.7, 0.8, etc). Then, I want to 1) make a table for the
results of B0[200], B1[200], and B2[200] for all values of p1 and 2)
make plots of B0, B1, B2 through time for the different values of p1.
Below is the code I tried. The table seems to work sometimes but when
I run the code multiple times, the output is the same for all values
of p1 (i.e., {{3.99315, 3.99315, 3.99315, 3.99315, 3.99315, 3.99315},
{
    0.0813405, 0.0813405, 0.0813405, 0.0813405, 0.0813405,
   0.0813405}, {0.021349, 0.021349, 0.021349, 0.021349, 0.021349,
0.021349}}. I don't understand why?
The Plot function gives me multiple plots but they are always the
same, so it is not drawing plots for the different values of p1.

J = 1;
r0 = 0.2;
r1 = 0.2;
r2 = 0.2;
p1 = 0.1;

dB0 = J - r0*B0[t] - B0[t]*B1[t];
dB1 = p1*B0[t]*B1[t] - r1*B1[t] - B1[t]*B2[t];
dB2 = p2*B1[t]*B2[t] - r2*B2[t];

A = Flatten[Map[({B0[200], B1[200], B2[200]} /. # ) &,
sol = Table[NDSolve[{B0'[t] == dB0, B1'[t] == dB1, B2'[t] == dB2,
B0[0] == 1, B1[0] == 1, B2[0] == 1}, {B0, B1, B2},
{t, 0, 200}], {p1, 0.5, 1, 0.1}]], 1] // Transpose
Export["A.csv", A];
Do[Plot[Evaluate[{B0[t], B1[t], B2[t]} /. sol, {t, 0, 200}, PlotStyle -
>
{{RGBColor[1, 0, 0]}, {RGBColor[0, 1, 0]}, {RGBColor[0, 0, 1]}}]],
{p1, 0.5, 1, 0.1}]

Thanks!



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