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MathGroup Archive 2003

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Re: NDSolve question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44456] Re: NDSolve question
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Mon, 10 Nov 2003 19:55:40 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <boifd7$obn$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

your differnial equation becomes singular at this point
and the stepsize control reduces the step when the
solution arrive the singularity. You will ot be able
to jump over the singularity with a polynomial
based initial value solver. You can use the initial
value solver that base on rational approximations or you can
extedn the equation into the complex plane and try 
to make an amalytic continuation.

Regards
  Jens

Emmanuel Dechenaux wrote:
> 
> Hi,
> I have what probably is a very basic question. I'm trying to solve the
> complicated first order differential equation below. There is a singularity
> at zero (which is my initial condition). The equation is also highly
> non-linear. I'm not quite sure what to do. I used different initial
> conditions as well, but Mathematica stops very quickly at x=3...... even if
> I increase MaxSteps. Again, I'm not quite sure what to do. If someone could
> help me, that would be great. Thanks.
> Emmanuel
> (My apology if the mathematica input didn't paste cleanly).
> 
> r = 0.7
> solution =
> NDSolve[{ (y' )[x] == ( ((x - y[x]) )^ ((r) ) - (( (-y[x] )) )^ ((r) ) ) /
> (x* ((r) ) ((x - y[x]) )^ ((r - 1) ) + ((1000 - x) ) (( (-y[x] )) )^ ((r -
> 1) ) ), y[0] == 0}, y, {x, 0, 1000}, MaxSteps -> 100000]


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