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MathGroup Archive 2001

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Re: help me plz

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32164] Re: [mg32149] help me plz
  • From: Reza Malek-Madani <research at usna.edu>
  • Date: Mon, 31 Dec 2001 02:24:22 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Here is a numerical solution to your BVP but with infinity replaced with
100 (you can make this value larger if you wish). The approximation uses
the shooting method, FindRoot and NDSolve.

Reza.

**********************************
$TextStyle = {FontFamily -> "Times", FontSize -> 14};
mylabel[x_] := StyleForm[TraditionalForm[x]];
F[b_] := Module[{sol, result},
sol = NDSolve[{y'[x] == yp[x],
               yp'[x] == ypp[x],
               ypp'[x] == -1/2 yp[x]ypp[x],
               y[0] == 0, yp[0] == 0, ypp[0] == b}, {y, yp, ypp},
               {x, 0, 100}, MaxSteps -> 1000000];
       result = First[Evaluate[yp[x] /. sol /. x -> 100]]];

shoot = FindRoot[F[b] - 1, {b, 0.1, 0.2}];
sol = NDSolve[{y'[x] == yp[x],
               yp'[x] == ypp[x],
               ypp'[x] == -1/2 yp[x]ypp[x],
               y[0] == 0, yp[0] == 0, ypp[0] == b /. shoot}, {y, yp, ypp},
               {x, 0, 100}, MaxSteps -> 1000000];
newy[x_] = y[x] /. sol;
Plot[newy[x], {x, 0, 100}, PlotLabel -> "Graph of y"];

graph = Plot[yp[x] /. sol, {x, 0, 100},
      PlotLabel -> mylabel["Graph of yprime"], PlotRange -> All];




-------------------------------------------------------------------------
Reza Malek-Madani               Director of Research
Research Office, MS 10m         Phone: 410-293-2504 (FAX -2507)
589 McNair Road                 DSN:      281-2504
U.S. Naval Academy              Nimitz Room 17 in ERC
Annapolis MD 21402-5031         Email: research at usna.edu

--------------------------------------------------------------------------


On Sat, 29 Dec 2001, Samer wrote:

>
> i want to solve this equation
>
> y"*y'+2y"'=0
>
> y(0)=0
> y'(0)=0
> y'(infini)=1
>



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