NDSolve and Parametric Plot

[Alex Cloninger]

So I'm trying to run a simple program that will solve this series of differential equations and plot the the x[t] function in the complex plane. Here's my code.

solution = NDSolve[{x'[t] == 2p[t], x[0] == 2, p'[t] == -2x[t], p[0] == Sqrt[-3]}, {x, p}, {t, 0, 2*π}]

repart[t_] := Re[x[t] /. solution]
impart[t_] := Im[x[t] /. solution]

ParametricPlot[{repart[t], impart[t]}, {t, 0, 2π}, PlotRange -> {{-2, 2}, {-2,2}}]

For some reason, when I go to plot the curve, I get an error saying
ParametricPlot::pptr: {repart[t], impart[t]} does not evaluate to a pair of real numbers at t=2.617993877991494`*^-7

What's going on? Could someone please help me with this?

[Bob Hanlon]

Delete the outer braces

solution =
NDSolve[{x'[t] == 2 p[t], x[0] == 2, p'[t] == -2 x[t],
p[0] == Sqrt[-3]}, {x, p}, {t, 0, Pi}][[1]];

repart[t_] := Re[x[t] /. solution]
impart[t_] := Im[x[t] /. solution]

ParametricPlot[{repart[t], impart[t]}, {t, 0, Pi},

PlotRange -> {{-2, 2}, {-2, 2}}]

This can also be solved exactly

solution =
DSolve[{x'[t] == 2 p[t], x[0] == 2, p'[t] == -2 x[t], p[0] ==

= Sqrt[-3]}, {x,

p}, t][[1]]

{x -> Function[{t}, 2*Cos[2*t] + I*Sqrt[3]*Sin[2*t]],
p -> Function[{t}, I*(Sqrt[3]*Cos[2*t] +
2*I*Sin[2*t])]}

Bob Hanlon

---- Alex Cloninger <aclon...@wustl.edu> wrote:
> So I'm trying to run a simple program that will solve this series of diff=
erential equations and plot the the x[t] function in the complex plane. He=
re's my code.
>
> solution = NDSolve[{x'[t] == 2p[t], x[0] == 2, p'[t] == -2x=
[t], p[0] == Sqrt[-3]}, {x, p}, {t, 0, 2*=CF=80}]

>
> repart[t_] := Re[x[t] /. solution]
> impart[t_] := Im[x[t] /. solution]
>

> ParametricPlot[{repart[t], impart[t]}, {t, 0, 2=CF=80}, PlotRange -> {{-2=

, 2}, {-2,2}}]
>
> For some reason, when I go to plot the curve, I get an error saying

> ParametricPlot::pptr: {repart[t], impart[t]} does not evaluate to a pair =

[Steve Luttrell]

You need to select the first solution by using [[1]]:

repart[t_] := Re[x[t] /. solution[[1]]]
impart[t_] := Im[x[t] /. solution[[1]]]

Stephen Luttrell
West Malvern, UK

"Alex Cloninger" <aclon...@wustl.edu> wrote in message
news:fomjh1$hmn$1...@smc.vnet.net...

> So I'm trying to run a simple program that will solve this series of
> differential equations and plot the the x[t] function in the complex
> plane. Here's my code.
>
> solution = NDSolve[{x'[t] == 2p[t], x[0] == 2, p'[t] == -2x[t], p[0] ==

> Sqrt[-3]}, {x, p}, {t, 0, 2*Ï?}]

>
> repart[t_] := Re[x[t] /. solution]
> impart[t_] := Im[x[t] /. solution]
>

> ParametricPlot[{repart[t], impart[t]}, {t, 0, 2Ï?}, PlotRange -> {{-2, 2},

[janos]

On febr. 10, 11:26, Alex Cloninger <aclonin...@wustl.edu> wrote:
> So I'm trying to run a simple program that will solve this series of diffe=
rential equations and plot the the x[t] function in the complex plane. Here=
's my code.
>
> solution = NDSolve[{x'[t] == 2p[t], x[0] == 2, p'[t] == -2x[=
t], p[0] == Sqrt[-3]}, {x, p}, {t, 0, 2*=F0}]

>
> repart[t_] := Re[x[t] /. solution]
> impart[t_] := Im[x[t] /. solution]
>

> ParametricPlot[{repart[t], impart[t]}, {t, 0, 2=F0}, PlotRange -> {{-2, 2}=

, {-2,2}}]
>
> For some reason, when I go to plot the curve, I get an error saying

> ParametricPlot::pptr: {repart[t], impart[t]} does not evaluate to a pair o=

f real numbers at t=2.617993877991494`*^-7
>
> What's going on? Could someone please help me with this?

Try
ParametricPlot[
Evaluate[{repart[t], impart[t]} /. solution], {t, 0, 2 \[Pi]}]

Hope, it helps,

Janos

[Peter Breitfeld]

Alex Cloninger schrieb:

You should write:
repart:=Re[ x[t]/.solution[[1]] ]
impart:=Im[ x[t]/.solution[[1]] ]

ParametricPlot[{repart,impart},{t,0,2Pi}]

Gruss Peter
--
==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

[Jens-Peer Kuska]

Hi,

solution =
NDSolve[{x'[t] == 2 p[t], x[0] == 2, p'[t] == -2 x[t],
p[0] == Sqrt[-3]}, {x[t], p[t]}, {t, 0, 2*Pi}];

repart[tau_] := (Re[x[t] /. solution[[1]]] ) /. t -> tau
impart[tau_] := (Im[x[t] /. solution[[1]]] ) /. t -> tau

ParametricPlot[{repart[t], impart[t]}, {t, 0, 2 Pi},

PlotRange -> {{-2, 2}, {-2, 2}}]

may help.

Regards
Jens

Alex Cloninger wrote:
> So I'm trying to run a simple program that will solve this series of di=
fferential equations and plot the the x[t] function in the complex plane.=
Here's my code.
>
> solution = NDSolve[{x'[t] == 2p[t], x[0] == 2, p'[t] == -=
2x[t], p[0] == Sqrt[-3]}, {x, p}, {t, 0, 2*=CF=80}]

>
> repart[t_] := Re[x[t] /. solution]
> impart[t_] := Im[x[t] /. solution]
>

> ParametricPlot[{repart[t], impart[t]}, {t, 0, 2=CF=80}, PlotRange -> {{=

-2, 2}, {-2,2}}]
>
> For some reason, when I go to plot the curve, I get an error saying

> ParametricPlot::pptr: {repart[t], impart[t]} does not evaluate to a pai=