RE: Re: odd behavior of NDSolv
- To: mathgroup@smc.vnet.net
- Subject: [mg11745] RE: [mg11624] Re: odd behavior of NDSolv
- From: Ersek_Ted%PAX1A@mr.nawcad.navy.mil
- Date: Thu, 26 Mar 1998 03:09:12 -0500
The information below indicates a non-default for the MaxStepSize option
can be used to fix the problem. NDSolve has several options that I
barely understand, and I suspect many other users are just as bad off.
The NDSolve options (with default settings) that give me trouble are:
DifferenceOrder -> Automatic,
MaxRelativeStepSize -> 1,
MaxStepSize -> Infinity,
Method -> Automatic,
SolveDelayed -> False,
StartingStepSize -> Automatic,
StoppingTest -> None
Has a tutorial been written to demonstrate when non default settings for
these options are useful? If not it would be a good topic.
Ted Ersek
----------
|From: "paul"@physics.uwa.edu.au@PMDF@PAXMB1 To: mathgroup@smc.vnet.net
|To: ersek ted; "mathgroup"@smc.vnet.net@PMDF@PAXMB1 |Subject: [mg11745] [mg11624]
Re: odd behavior of NDSolve |Date: Friday, March 20, 1998 12:35AM |
|<<File Attachment: 00000000.TXT>>
|Selwyn Hollis wrote:
|
|> I've discovered a very disturbing problem with NDSolve. I'd like to
know |> if others can reproduce this.
|>
|> f[x_, y_] := 1 - Exp[-(x^2 + y^2)] |> fx[x_, y_] = D[f[x, y], x];
fy[x_, y_] = D[f[x, y], y]; |> Clear[x0, y0, u0, v0];
|> diffeqs =
|> {x''[t] == -fx[x[t], y[t]],
|> y''[t] == -fy[x[t], y[t]],
|> x[0] == x0, x'[0] == u0, y[0] == y0, y'[0] == v0} |> endTime =
12.03;
|> {x0, y0, u0, v0} = {4, 3, -0.7, -0.17}; |> soln =
Flatten[NDSolve[diffeqs, {x, y}, {t, 0, endTime}]]; |> r[t_] = {x[t],
y[t]} /. soln;
|> path = ParametricPlot[r[t], {t, 0, endTime}, |> PlotRange ->
{{-4, 4}, {-4, 4}}]; |>
|> You should see a curve with a slight bend to it. Now change endTime
to |> 12.04. The bend is gone. Shouldn't we get the same curve for 0 <
t < |> 12.03? Either I'm missing something or NDSolve has a serious
problem. |
|The problem is that the NDSolve default setting of MaxStepSize is
|Infinity. If you manually change this, the problem goes away, e.g., |
| soln = Flatten[NDSolve[diffeqs, {x, y}, {t, 0,
|endTime},MaxStepSize->1]];
|
|Cheers,
| Paul
|
|____________________________________________________________________
|Paul Abbott Phone: +61-8-9380-2734
|Department of Physics Fax: +61-8-9380-1014
|The University of Western Australia Nedlands WA 6907
|mailto:paul@physics.uwa.edu.au AUSTRALIA
|http://www.pd.uwa.edu.au/~paul
|
| God IS a weakly left-handed dice player
|____________________________________________________________________ |