       Re: NDSolve problem

• To: mathgroup at smc.vnet.net
• Subject: [mg31817] Re: NDSolve problem
• From: Roland Franzius <Roland.franzius at Uos.de>
• Date: Wed, 5 Dec 2001 06:51:39 -0500 (EST)
• Organization: Uni Osnabrueck
• References: <9u4gqb\$lpb\$1@smc.vnet.net> <9ua1tk\$13v\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```If the system of ODE's has a critical point somewhere, say at x=a,  it should
always be possible, to extract the singularilty by the ansatz  of critical
exponents
y_i  = (x-a)^(s_i)   z_i(x), i=1,..n
in such a way that the resulting system for z is smooth or L^1 or something like
that. At least one solution should be well behaved at this point then.

Jens-Peer Kuska wrote:

> Hi,
>
> your system of equations has a singularity at this point
> and one of the components goes to infinity. The stepsize
> control detect the singularity and reduce the stepsize
> until it is to small.
>
> You should care full analyse the differential equation
> if the singularity is not expected/obvious.
>
> With an ordinary differntial equations solver it is
> impossible to jump over the singularity, because
> the most ode solver use a polynomial approximation
> to the solution and you can't approximate  1/x with
> a polynomial of positive powers.
>
> Regards
>   Jens
>
> deniz.seker at arcelik.com.tr wrote:
> >
> > Hi,
> >
> > I have a problem with NDSolve. I'm trying to solve 2 coupled differential
> > equations. But dur,ng the solution, I saw a message that,"At t=.... step
> > size is effect,vely zero, singularity suspected." Then, I'm trying to
> > decrease StartingStepSize option up to 10^(-14) or increase MaxSteps to
> > 100000. But, for these two cases, I couldn't get solutions for 6 hours run.
> > What should I do?
> >
> > Best regards,
> >
> > Deniz
> >
> > PS : If anybody wants to see the notebook, I can send via e-mail.

--
Roland Franzius

```

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