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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*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[0] == 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[0] == c}, > y, {t, -10, 10}][[1]]) > > 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[0] == c}, > >> y[t], {t, -10, 10}][[1]] /. t -> x > >> > >> Manipulate[Plot[ > >> Evaluate[func[coef, c, x] /. c -> Range[5]], > >> {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: > >> > Thanks for your answer Bob, > >> > 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[0] == c}, y[x], x][[1]] // > >> >> Simplify > >> >> > >> >> c + Sin[coef*x]/coef > >> >> > >> >> > >> >> Manipulate[Plot[Evaluate[ > >> >> func[coef, c, x] /. > >> >> c -> Range[5]], > >> >> {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[1] -> {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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**Re: Manipulate a Plot of Evaluate DSolve**

**Re: Manipulate a Plot of Evaluate DSolve**

**Re: Manipulate a Plot of Evaluate DSolve**