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06/28/12 7:24pm

Author later posted a longer version:

=====
I have a set of coupled Differential Equations:

\[Beta]'[t] == (Sqrt[3/2]*\[Alpha]^2*T[t]^(11/2))/m^(9/2)*(bb^2 - \[Beta][t]^2

T'[t] == (Sqrt[g]*T[t]^3)/(Sqrt[3]*M)

with these conditions:
M = 10000;
g = 1;
\[Alpha] = 1;
A = 10;
a = 0;(*initial plot temp*)
b = .001; (*final plot temp*)
c = .01; (*initial temp*)
d = 0; (*initial \[Beta]*)
m = .001;

*Although the limits a and b can be manipulated to show the results best.


What I want to do now not only solve this set of coupled differential equations but also generate a plot for \[Beta] as a function of T. I have B[t] and T[t] and what I want now is to generate a plot of B[t] from these equations.


I have tried this;

s = NDSolve[{\[Beta]'[t] == (Sqrt[3/2]*\[Alpha]^2*T[t]^(11/2))/m^(
9/2)*(bb^2 - \[Beta][t]^2),
T'[t] == (Sqrt[g]*T[t]^3)/(Sqrt[3]*M), \[Beta][0] == 0,
T[0] == c}, {\[Beta][t], T[t]}, {t, a, b}];
ParametricPlot[{(Evaluate[{T[t], \[Beta][t]} /. s])}, {t, a, b},
PlotRange -> Automatic]

But I can't seem to generate anything coherent.



Ideally this set of equations should regenerate the plots produced by:

M = 10000;
g = 1;
\[Alpha] = 1;
A = 10;
a = .01;(*initial plot temp*)
b = 1.2; (*final plot temp*)
c = 0.00000001; (*initial temp*)
d = 0; (*initial \[Beta]*)
m = 1;
bb = (g/(2*\[Pi])^(3/2)*(m/T)^(3/2)*E^(-m/T));

s = NDSolve[{\[Beta]'[T] == (3*\[Alpha]^2*M*T^(5/2))/(
Sqrt[2*g]*m^(9/2))*(bb^2 - \[Beta][T]^2), \[Beta][c] ==
d}, \[Beta], {T, a, b}, Method -> "BDF"];

Plot[{(Evaluate[\[Beta][T] /. s])/bb}, {T, a, b},
PlotRange -> Automatic]


Any and all help would be much appreciated!!!




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Subject (listing for 'Solving Coupled Diff Eqs ( Simple )')
Author Date Posted
Solving Coupled Diff Eqs ( Simple ) William Duhe 06/27/12 11:55am
Re: Solving Coupled Diff Eqs ( Simple ) Forum Modera... 06/28/12 7:24pm
Re: Re: Solving Coupled Diff Eqs ( Simple ) Michael 06/30/12 6:09pm
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