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From: susy on 19 May 2010 07:03
Hallo,

I need to solve the following differential equation:

(1/4 r^2 + 2 Sin[F[r]]^2) F''[r] + 1/2 r F'[r] +
Sin[2 F[r]] (F'[r])^2 - 1/4 Sin[2 F[r]] - (Sin[F[r]]^2 Sin[2 F[r]])/r^2 == 0

with boundary values:
F[0]==Pi, F[Infinity]==0.

I tried NDSolve, but failed to get a solution.
How can I solve that equation?

Best regards,
susy

From: Narasimham on 19 May 2010 20:13
I suppose some insight into the behavior of F[r] is required to avoid
singularities.The following works for different BC.

NDSolve[{1/4 r^2 + 2 Sin[F[r]]^2 F''[r] + 1/2 r F'[r] +
Sin[2 F[r]] F'[r]^2 -
1/4 Sin[2 F[r]] - (Sin[F[r]]^2 Sin[2 F[r]])/r^2 == 0,
F[10^-5] == Pi/2, F'[10^-5] == 0}, F, {r, 10^-5, 18.12}]
f[u_] = F[u] /. First[%]; Plot[f[r], {r, 10^-5, 18.12}]

Narasimham

May 19, 4:03 pm, susy <fengk...(a)gmail.com> wrote:
> Hallo,
>
> I need to solve the following differential equation:
>
> (1/4 r^2 + 2 Sin[F[r]]^2) F''[r] + 1/2 r F'[r] +
> Sin[2 F[r]] (F'[r])^2 - 1/4 Sin[2 F[r]] - (Sin[F[r]]^2 Sin[2 F[r]])/r=
^2 == 0
>
> with boundary values:
> F[0]==Pi, F[Infinity]==0.
>
> I tried NDSolve, but failed to get a solution.
> How can I solve that equation?
>
> Best regards,
> susy


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