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] > > >