MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

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}]


  • Prev by Date: Data structure for Earth slice data
  • Next by Date: Re: Manipulate slider moves from top to side
  • Previous by thread: RE: Data structure for Earth slice data
  • Next by thread: Re: NDSolve - Nice function but stiffness-problem