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}]
>