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