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=

**References**:**How to Scale and vary plot for a Differential Equation***From:*Rahul Chakraborty <rahul.6sept@gmail.com>