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Re: How to Scale and vary plot for a Differential Equation
*To*: mathgroup at smc.vnet.net
*Subject*: [mg127414] Re: How to Scale and vary plot for a Differential Equation
*From*: Bob Hanlon <hanlonr357 at gmail.com>
*Date*: Mon, 23 Jul 2012 01:04:12 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: mathgroup-newout@smc.vnet.net
*Delivered-to*: mathgroup-newsend@smc.vnet.net
*References*: <20120720074852.62B9B685F@smc.vnet.net>
I do not see any of these problems on my system.
$Version
"8.0 for Mac OS X x86 (64-bit) (October 5, 2011)"
Bob Hanlon
On Sun, Jul 22, 2012 at 2:03 PM, Rahul Chakraborty
<rahul.6sept at gmail.com> wrote:
> Dear Sir,
>
> 1). Regarding the last program of plotting DE there is one problem
> that i'm facing.The issue is, when i open the file first time the
> program shows lots of errors which vanishes after i run the program
> using Shift + Enter. I close the file and reopens the errors appears
> again.
>
> The list of errors as under:
>
> NDSolve::deqn: Equation or list of equations expected instead of True
> in the first argument {0.\[VeryThinSpace]+0.5[t]==0,0.5[0]==1/2,T=
rue}
> . >>
>
> ReplaceAll::reps: {0.\[VeryThinSpace]+0.5[t]==0,0.5[0]==1/2,True}
> is neither a list of replacement rules nor a valid dispatch table,
> and so cannot be used for replacing. >>
>
> ReplaceAll::reps: {0.\[VeryThinSpace]+0.5[t]==0,0.5[0]==1/2,True}
> is neither a list of replacement rules nor a valid dispatch table,
> and so cannot be used for replacing. >>
>
> ReplaceAll::reps: {0.\[VeryThinSpace]+0.5[0.]==0,0.5[0]==1/2,True=
}
> is neither a list of replacement rules nor a valid dispatch table,
> and so cannot be used for replacing. >>
>
> General::stop: Further output of ReplaceAll::reps will be suppressed
> during this calculation. >>
>
> General::ivar: 0.00033557046979865775` is not a valid variable. >>
>
> General::ivar: 0.00033557046979865775` is not a valid variable. >>
>
> General::ivar: 0.3359060402684564` is not a valid variable. >>
>
> General::stop: Further output of General::ivar will be suppressed
> during this calculation. >>
>
>
>
> 2). Also in case of the previous plot of 1st order DE there appers a w=
arning
>
> K$$::shdw: Symbol K$$ appears in multiple contexts {System`,Global`};
> definitions in context System` may shadow or be shadowed by other
> definitions. >>
>
> and the variable K appears as Global` K and it does not increment in
> Autorun mode.
>
>
> Kindly advice me.
>
>
> Regards,
>
> rc
>
>
> On 7/22/12, Bob Hanlon <hanlonr357 at gmail.com> wrote:
>> DSolve[{x''[t] + \[Mu] (x[t] x[t] - 1) x'[t] + x[t] == 0, x[0] ==
= 1/2,
>> x'[0] == 0}, x[t], t][[1]]
>>
>> {x[t] + \[Mu]*(-1 + x[t]^2)*
>> Derivative[1][x][t] +
>> Derivative[2][x][t] == 0,
>> x[0] == 1/2, Derivative[1][x][
>> 0] == 0}
>>
>> In this case, DSolve did not solve the DE (returned unevaluated) so
>> NDSolve must be used. To use NDSolve, \[Mu] must have a numeric
>> value so the NDSolve must be inside of the Manipulate.
>>
>> Manipulate[sol = NDSolve[
>> {x''[t] + \[Mu] (x[t] x[t] - 1) x'[t] + x[t] == 0,
>> x[0] == 1/2, x'[0] == 0}, x[t],
>> {t, 0, 50}][[1]];
>> ParametricPlot[Evaluate[
>> {x[t] /. sol, Log[D[x[t] /. sol, t]]}],
>> {t, 0, 50},
>> Frame -> True,
>> Axes -> False,
>> FrameLabel -> {"x", Overscript["x", "."]}, AspectRatio -> 1,
>> PlotRange -> {{0, 2.5}, {-6, 4.5}},
>> PlotPoints -> 150],
>> {{\[Mu], 1}, 1, 50, 0.1,
>> Appearance -> "Labeled"}]
>>
>>
>> Bob Hanlon
>>
>>
>> On Sat, Jul 21, 2012 at 1:20 PM, Rahul Chakraborty
>> <rahul.6sept at gmail.com> wrote:
>>> Dear Bob,
>>>
>>> Sir, I've tried the same code for another DE. Everything is same just
>>> changed the equations and initial conditions. Its giving an error, i
>>> couldn't debug it.
>>>
>>> Clear[x];
>>> DSolve[{x''[t]+\[Mu]
>>> (x[t]x[t]-1)x'[t]+x[t]==0,x[0]==1/2,x'[0]==0},x[t],t][[1]]/=
/Quiet
>>> {x[t]->x[t]+\[Mu] (-1+x[t]^2)
>>> (x^\[Prime])[t]+(x^\[Prime]\[Prime])[t]==0,x[0]==1/2,x'[0]==
=0}
>>> Manipulate[Module[{sol},sol={x[t]->{x[t]+\[Mu] (-1+x[t]^2)
>>> (x^\[Prime])[t]+(x^\[Prime]\[Prime])[t]==0,x[0]==1/2,x'[0]==
=0}};ParametricPlot[Evaluate[{x[t]/.sol,Log[D[x[t]/.sol,t]]}],{t,0,50},Fr=
ame->True,Axes->False,FrameLabel->{"x",Log[Overscript[x,"."]]},AspectRatio-=
>1,PlotRange->{{0,10.1},{-6,10.1}}]],{{\[Mu],1},1,50,0.01,Appearance->"Labe=
led"}]
>>>
>>> ERROR: ParametricPlot::exclul: {Im[(x^\[Prime])[t]+2 x[t]
>>> (<<1>>^(<<1>>))[<<1>>]^2+(-1+Power[<<2>>])
>>> (x^\[Prime]\[Prime])[t]+(x^(3))[t]==0]-0} must be a list of equalit=
ies
>>> or real-valued functions. >>
>>>
>>> Kindly advice.
>>>
>>> Regards,
>>>
>>> rc
>>>
>>> On 7/21/12, Bob Hanlon <hanlonr357 at gmail.com> wrote:
>>>> It is not required. If you don't like it, don't use it. Adjust
>>>> PlotRange to taste.
>>>>
>>>>
>>>> Bob Hanlon
>>>>
>>>>
>>>> On Sat, Jul 21, 2012 at 12:57 AM, Rahul Chakraborty
>>>> <rahul.6sept at gmail.com> wrote:
>>>>> Dear Bob,
>>>>>
>>>>> Thanks.
>>>>>
>>>>> But one query, why it is required to use Log in " Log[D[x[t] /. sol=
,
>>>>> t]". Because in simple plot without Manipulate it is not required.
>>>>>
>>>>>
>>>>> Regards,
>>>>> rc
>>>>>
>>>>> On 7/21/12, Bob Hanlon <hanlonr357 at gmail.com> wrote:
>>>>>> You appear to be confusing the syntax of DSolve with that of NDSolve=
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