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Re: NDSolve - Nice function but stiffness-problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94095] Re: NDSolve - Nice function but stiffness-problem
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 5 Dec 2008 05:27:30 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <gh8hih$qv5$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

for larger A, f[x] change the sign and than no solution
for the boundary value problem exist any more.
Mathematica report the x position where f[x] become
negative.

Regards
   Jens

Nano wrote:
> Hello, 
> 
> I want to solve a non-linear differential equation using mathematica. The equation is:
> 
> f''[x] = Exp[A * f[x]]
> 
> Using the NDSolve in a normal way does only work for a small value of A (A<2.3). The message 
> 
> "NDSolve::ndsz: At x == 0.7735551758505442`, step size is effectively \
> zero; singularity or stiff system suspected" 
> 
> appears. Looking at the graph I can not really see a problem at this value of A. It still looks like a "nice" function. I tried changing the method (-> StiffnessSwitching) and the accuracy, stepsize,... but nothing really helped.
> 
> Where is the problem? 
> It is hard to believe for me that Mathematica can not handle it.
> 
> Here the problem as Copy&Paste for Mathematica 6: 
> 
> Solution[A_] := 
> NDSolve[{D[\[Phi][x], {x, 2}] == Exp[A * \[Phi][x]], \[Phi]'[1] == 
> 0, \[Phi][0] == 1}, \[Phi][x], {x, 0, 1}] 
> Manipulate[ 
> Plot[Evaluate[\[Phi][x] /. Solution[A]], {x, 0, 1}, 
> PlotRange -> {0, 1}], {A, 0, 10}]
> 


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