NDSolve - Nice function but stiffness-problem
- To: mathgroup at smc.vnet.net
- Subject: [mg94070] NDSolve - Nice function but stiffness-problem
- From: Nano <lukas.kranz at gmx.de>
- Date: Thu, 4 Dec 2008 07:14:06 -0500 (EST)
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}]