       Re: Manipulate a Plot of Evaluate DSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg127522] Re: Manipulate a Plot of Evaluate DSolve
• From: Juan Barandiaran <barandiaran.juan at gmail.com>
• Date: Wed, 1 Aug 2012 04:56:10 -0400 (EDT)
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• References: <20120729070521.C7CB3684D@smc.vnet.net> <CAEtRDSfuzxN12HoeTLPuZGmegBOpubxd3J_g0ESgnT8=KQStBw@mail.gmail.com>

```Thanks again Bob,

It looks a promising approach as it works and has the differential equation
outside the Manipulate and Plot blocks.
The only problem that I find now is that this solution is incredibly slow
as soon as you include it in a list of Plots.
I'll give a simple example, of the model I'm building of some objects
moving in the sea waves.

First a simple user interface taking advantage of the great options we have
in Manipulate and Plot:

ClearAll["Global`*"];

Manipulate[
Plot[
{n0*Sin[coef*x + time], -H2, H1,
n0*Sin[coef*x + time] + c /. c -> Range[-5, -1]},
{x, -XMax, XMax}, AxesLabel -> {"X", "Y"},
Filling -> {1 -> {{2}, LightBlue}}, PlotRange -> {-H2, H1},
AspectRatio -> Automatic,
PlotLabel -> "Floating object in Sea Wave Model"],
{{time, 0, "Time"}, 0, 5*2*Pi,
Appearance -> "Labeled"}, {{coef , 1, "Wave Frequency"}, 0.1, 5,
Appearance -> "Labeled"}, {{n0, 0.5, "Wave Amplitude"}, 0.1, 5,
Appearance -> "Labeled"}, {{H1, 3, "Air Height"}, 1, 10,
Appearance -> "Labeled"}, {{H2, 10, "Water Depth"}, 1, 50,
Appearance -> "Labeled"}, {{XMax, 10}, 1, 50,
Appearance -> "Labeled"}, ControlPlacement -> Right]

If you move the sliders of Manipulate it works fast and is responsive.

Then we add a simple differential equation with the proposed solution:

func[coef_?NumericQ, c_?NumericQ,
xLim_?NumericQ] := (y[t] /.
NDSolve[{y'[t] == Cos[coef*t], y == c}, y, {t, -xLim, xLim}][[
1]])

Manipulate[
Plot[Evaluate[
Table[func[coef, c, 10] /. t -> x, {c, -5, -1}]], {x, -10, 10},
PlotRange -> {-10, 5}], {{coef, 1}, 0.1, 5, 0.01,
Appearance -> "Labeled"}]

It continues to work fast. So far so good.

Now we try to integrate both things in a Manipulate block (or a Plot, I
don't think the problem is with manipulate):

Manipulate[
Plot[
{n0*Sin[coef*x + time], -H2, H1,
Evaluate[Table[func[coef, c, XMax] /. t -> x, {c, -5, -1}]]},
{x, -XMax, XMax}, AxesLabel -> {"X", "Y"},
Filling -> {1 -> {{2}, LightBlue}}, PlotRange -> {-H2, H1},
AspectRatio -> Automatic,
PlotLabel -> "Floating object in Sea Wave Model"],
{{time, 0, "Time"}, 0, 5*2*Pi,
Appearance -> "Labeled"}, {{coef , 1, "Wave Frequency"}, 0.1, 5,
Appearance -> "Labeled"}, {{n0, 1, "Wave Amplitude"}, 0.1, 5,
Appearance -> "Labeled"}, {{H1, 3, "Air Height"}, 1, 10,
Appearance -> "Labeled"}, {{H2, 10, "Water Depth"}, 1, 50,
Appearance -> "Labeled"}, {{XMax, 10}, 1, 50,
Appearance -> "Labeled"}, ControlPlacement -> Right]

And at least in my system, the interface becomes incredibly slow... WHY
???? Any workaround? Is it necessary to use a Table?

Thanks once more and best regards,

Juan

2012/7/31 Bob Hanlon <hanlonr357 at gmail.com>

> Not sure what happened. Try this
>
> Clear[func]
>
> func[coef_?NumericQ, c_?NumericQ] :=
>  (y[t] /. NDSolve[
>      {y'[t] == Cos[coef*t], y == c},
>      y, {t, -10, 10}][])
>
> Manipulate[
>  Plot[
>   Evaluate[
>    Table[
>     func[coef, c] /. t -> x,
>     {c, 5}]],
>   {x, -10, 10},
>   PlotRange -> {-5, 10}],
>  {{coef, 1}, 0.1, 5, 0.01,
>   Appearance -> "Labeled"}]
>
>
> Bob Hanlon
>
>
> On Mon, Jul 30, 2012 at 9:17 PM, Juan Barandiaran
> <barandiaran.juan at gmail.com> wrote:
> > Thanks Bob,
> >
> > Yes, I could use NDSolve instead of DSolve, in my case I'm only getting
> > numerical outputs, so it should do the job.
> >
> > But in the example that you send me, why is nothing plotted?
> >
> > Thanks again and best regards,
> >
> > Juan
> >
> >
> > 2012/7/30 Bob Hanlon <hanlonr357 at gmail.com>
> >>
> >> If DSolve cannot solve the equations then use NDSolve.
> >>
> >> func[coef_?NumericQ, c_?NumericQ, x_?NumericQ] :=
> >>  y[t] /. NDSolve[{y'[t] == Cos[coef*t], y == c},
> >>      y[t], {t, -10, 10}][] /. t -> x
> >>
> >> Manipulate[Plot[
> >>   Evaluate[func[coef, c, x] /. c -> Range],
> >>   {x, -10, 10},
> >>   PlotRange -> {-5, 10}],
> >>  {{coef, 1}, 0.1, 5, 0.01,
> >>   Appearance -> "Labeled"}]
> >>
> >>
> >> Bob Hanlon
> >>
> >>
> >> On Sun, Jul 29, 2012 at 6:12 PM, Juan Barandiaran
> >> <barandiaran.juan at gmail.com> wrote:
> >> > Of course your solution works, but I still don't understand why mine
> >> > doesn't
> >> > and I cannot use your proposed approach because the way you write the
> >> > problem it is easy for Mathematica to solve the DSolve.
> >> > And this is just a simple example, in my real problem the DSolve
> cannot
> >> > be
> >> > solved analytically.
> >> > This is why I tried to express the function as:
> >> >
> >> > {{y -> Function[{x}, DSolve[y'[x] == Cos[coef *x], y, x]]}}
> >> >
> >> > , which is something like the output I get from my DSolve.
> >> >
> >> > Thanks for your help.
> >> >
> >> > Juan
> >> >
> >> >
> >> > 2012/7/29 Bob Hanlon <hanlonr357 at gmail.com>
> >> >>
> >> >> Clear[func];
> >> >>
> >> >> func[coef_, c_, x_] =
> >> >>  y[x] /. DSolve[{y'[x] == Cos[coef*x], y == c}, y[x], x][] //
> >> >>   Simplify
> >> >>
> >> >> c + Sin[coef*x]/coef
> >> >>
> >> >>
> >> >> Manipulate[Plot[Evaluate[
> >> >>    func[coef, c, x] /.
> >> >>     c -> Range],
> >> >>   {x, -10, 10},
> >> >>   PlotRange -> {-5, 10}],
> >> >>  {{coef, 1}, 0.1, 5, 0.01,
> >> >>   Appearance -> "Labeled"}]
> >> >>
> >> >>
> >> >> Bob Hanlon
> >> >>
> >> >>
> >> >> On Sun, Jul 29, 2012 at 3:05 AM,  <barandiaran.juan at gmail.com>
> wrote:
> >> >> > Hi,
> >> >> >
> >> >> > I'm trying to Manipulate a Plot of a quite difficult function which
> >> >> > involves solving a differential equation, but cannot be solved
> >> >> > analytically.
> >> >> >
> >> >> > To try to simplify the example and simulate it, let's assume that
> we
> >> >> > have the following function:
> >> >> >
> >> >> > func[coef_] = {{y -> Function[{x}, DSolve[y'[x] == Cos[coef *x], y,
> >> >> > x]]}}
> >> >> >
> >> >> > Manipulate[Plot[{{Evaluate[y[x] /. func[coef] /. C -> {Range[-5,
> >> >> > 0]}]}}, {x, -10, 10}], {{coef , 1}, 0.1, 5}]
> >> >> >
> >> >> > I get an error: DSolve::dsvar: "-9.99959 cannot be used as a
> >> >> > variable"
> >> >> >
> >> >> > I think that this is because Manipulate assigns a value to x (=
> >> >> > -9.99959) BEFORE solving the DSolve, even though to avoid it I'm
> >> >> > using the
> >> >> > Evaluate function, which should process the function before
> assigning
> >> >> > a
> >> >> > value to x.
> >> >> >
> >> >> > But the thing is that the "coef" to be Manipulated is at the same
> >> >> > "level" as the x in the Manipulate block, so probably if I need the
> >> >> > coef to
> >> >> > solve the DSolve, I also have the x that gives me an error.
> >> >> >
> >> >> > Is there any workaround? I guess I'm not understanding properly how
> >> >> > Mathematica processes these simple expressions.
> >> >> >
> >> >> > Thanks, Juan
> >> >> >
> >> >
> >> >
> >
> >
>

```

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