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Re: Numerical solution of differential equation with boundary values

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109850] Re: Numerical solution of differential equation with boundary values
  • From: Narasimham <mathma18 at hotmail.com>
  • Date: Wed, 19 May 2010 20:15:13 -0400 (EDT)
  • References: <ht0gi3$c1$1@smc.vnet.net>

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... at 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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