Re: Dr. Lynchs book Dynamical Systems with Applications using Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg125375] Re: Dr. Lynchs book Dynamical Systems with Applications using Mathematica
• From: "Kevin J. McCann" <kjm at KevinMcCann.com>
• Date: Sat, 10 Mar 2012 06:17:16 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <3203584.822.1331070143155.JavaMail.geo-discussion-forums@ynkz21> <jjcokk\$qam\$1@smc.vnet.net>

```You have a fairly large number of syntax issues. I am don't know how you
put the code into the email. It appears that your C5 and =C2=AE are
really something else. Here is the cleaned up code that works. I suggest
that when you copy Mathematica code for emailing purposes that you
highlight the code, right-click, and choose Copy As ->Input Text.

The code numerically solves the coupled DE with x0 and y0 as variable
IC's. sol[1], etc are the solutions in InterpolationFunctions. The
/.sol[i] uses rules to replace x and y in the ParametricPlot.

My suggestion is that you need to learn Mathematica before you read the
book.

Kevin

p1 = VectorPlot[{2 x + y, x + 2 y}, {x, -3, 3}, {y, -3, 3}];

ode1[x0_, y0_] :=
NDSolve[{x'[t] == 2 x[t] + y[t], y'[t] == x[t] + 2 y[t], x[0] == x0,
y[0] == y0}, {x[t], y[t]}, {t, -3, 3}];

sol[1] = ode1[1, 1]; sol[2] = ode1[1, -1]; sol[3] = ode1[-1, -1];
sol[4] = ode1[-1, 1];
sol[5] = ode1[3, 1]; sol[6] = ode1[1, 3]; sol[7] = ode1[-1, -3];
sol[8] = ode1[-3, -1];

p2 = ParametricPlot[
Evaluate[Table[{x[t], y[t]} /. sol[i], {i, 8}]], {t, -3, 3},
PlotRange -> {{-3, 3}, {-3, 3}}, PlotPoints -> 100,
AxesLabel -> {"x", "y"}];

Show[{p1, p2}, PlotRange -> {{-3, 3}, {-3, 3}},
AxesLabel -> {"x", "y"}, Axes -> True]

On 3/9/2012 6:13 AM, pennsylvaniajake at gmail.com wrote:
> Could some one please explain the code?
>
> The line starts with sol[1] and ends with ode1[-3,-4];
>
> I have looked through all my books on Mathematica and cannot find
> anything like it.
>
>   p1=VectorPlot[{2x+y,x+2y},{x,-3,3},{y,-3,3}] ;
>   ode1[x0_,y0_]:=NDSolve[{x'[t]=C5 2x[t]+y[t],y'[t]=C5 x[t]+2y[t],x[0]=C5 x0,y[0]=C5 y0},{x[t],y[t]},{t,-3,3}];
>
>   sol[1]=ode1[1,1];sol[2]=ode1[1,-1];sol[3]=ode1[-1,-1];sol[4]=ode1[-1,1];sol[5]=ode1[3,1];sol[6]=ode1[1,3];sol[7]=ode1[-1,-3];sol[8]=ode1[-3,-1];
>
>   p2=ParametricPlot[Evaluate[Table[{x[t],y[t]}/.sol[i],{i,8}]],{t,-3,3},
>   PlotRange=C2=AE{{-3,3},{-3,3}},PlotPoints=C2=AE100,AxesLabel=C2=AE{"x","y"}];
>
>   Show[{p1,p2},PlotRange=C2=AE{{-3,3},{-3,3}},AxesLabel=C2=AE{"x","y"},Axes=C2=AETrue]
>
>
>

```

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