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Student Support Forum: 'Varying Parameters with a Diff Eq.' topicStudent Support Forum > General > Archives > "Varying Parameters with a Diff Eq."

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Author Comment/Response
Michael
06/01/12 08:04am

0. You might have to clear/unset M to get the things below to work (Clear[M])

1. This seemed to be closest to what you had in mind, but there are other ways, below:

ListPlot3D[
Flatten[Table[
With[{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"]},
Table[{M, TT, First[\[Beta][T] /. s]/bb /. T -> TT}, {TT, a, b,
0.05}]], {M, .0, 10000, 100}], 1]]

2. ParametricPlot3D can be used to collate the individual plots, with M as one of the coordinates

With[{eqns =
Table[With[{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"]}, {M, T,
First[\[Beta][T] /. s]/bb}], {M, 0., 10000, 100}]},
ParametricPlot3D[eqns, {T, a, b},
PlotRange -> {{0, 10000}, {a, b}, Automatic},
PlotRangePadding -> Scaled[0.1], BoxRatios -> {1, 1, 0.4}]]

3. You can treat the DE as a PDE with M, T as independent variables.

Plot3D[Evaluate[\[Beta][T, M] /.
NDSolve[{D[\[Beta][T, M], T] == (3*\[Alpha]^2*M*T^(5/2))/(
Sqrt[2*g]*m^(9/2))*(bb^2 - \[Beta][T, M]^2), \[Beta][T, 0] ==
d, \[Beta][c, M] == d}, \[Beta], {T, a, b}, {M, 0., 10000.},
Method -> "BDF"]], {M, 0., 10000}, {T, a, b}, PlotPoints -> 24,
Mesh -> {20, 0}]


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Subject (listing for 'Varying Parameters with a Diff Eq.')
Author Date Posted
Varying Parameters with a Diff Eq. William Duhe 05/31/12 11:06am
Re: Varying Parameters with a Diff Eq. Michael 06/01/12 08:04am
Re: Re: Varying Parameters with a Diff Eq. William Duhe 06/06/12 11:21am
Re: Varying Parameters with a Diff Eq. Bill Simpson 06/01/12 12:10pm
Re: Varying Parameters with a Diff Eq. Bill Simpson 06/01/12 12:26pm
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