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NDSolve and vector variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63895] NDSolve and vector variables
  • From: "Borut Levart" <BoLe79 at gmail.com>
  • Date: Sat, 21 Jan 2006 01:50:42 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Mathematica users,

They say that NDSolve now supports vector variables. What does that
mean? (I have found an old thread,
http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_frm/thread/d0c58a1fb0cfc8a7/8ba36139dc6a2b88#8ba36139dc6a2b88,
but no one really answered the one who asked.)
I couldn't've found any examples in the Help Browser either, so I would
like to ask you if the below example (of throwing a stone under the
gravitaion and drag) shows this "vector-variables support", or could it
be rewritten more elegantly (in a vector-variables sense)?


r[t_]:={x[t],y[t]}

sol=
    Map[Function[{b2m},
        NDSolve[
            With[{g=9.8,v0=10,fi=.2 Pi},
              Thread[Equal[
                  Join[r''[t],r[0],r'[0]],{-b2m
Sqrt[r'[t].r'[t]],-g,0,0,v0 Cos[fi],v0 Sin[fi]}]
                ]],r[t],{t,0,10},
            StoppingTest->(y[t]<0)][[1]]],
      {0,1,2}];

<<Graphics`

With[{t2=sol[[1,2,-1,0,1,1,-1]]},
  DisplayTogether[
    ParametricPlot[
          Evaluate[{x[t],y[t]}/.#],{t,0,t2},
          PlotRange->{{0,10},{0,2}}]&/@sol
    ]]




Thank you for your considering,

Borut, Slovenia


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