NDSolve, Loop, Table, Plot

[Solver]

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!

[Jens-Peer Kuska]

Hi,

you can make a function, that take the parameters of
your ode as arguments, something like

sol[omega_] :=
Module[{f, y, x},
f = y[x] /.
NDSolve[{y''[x] + omega^2*y[x] == 0, y[0] == 0, y'[0] == 1},
y[x], {x, 0, 2 Pi}][[1]];
Table[{x, f}, {x, 0., 2 Pi, 2 Pi/128}]
]

and

ListPlot[{sol[1], sol[2], sol[3]}]

will do that or you can define Rule[]s for the parameter

NDSolve[{y''[x] + omega^2*y[x] == 0, y[0] == 0, y'[0] == 1},
y[x], {x, 0, 2 Pi}] /. {{omega -> 1}, {omega -> 2}, {omega -> 3}}

Regards
Jens

[dh]

Hi Solver

the variable p2 does not have a value. Presumably you wanted to write

p2=0.1 instead of p1=0.1.

If you are using version 6 you must additionally wrap the Plot statement

in a Print statement.

hope this helps, Daniel

[rob]

Sir, I tried your code but the ListPlot does not work. I'm
using V5.1.