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Re: NDSolve - how to bypass safety chceck?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111377] Re: NDSolve - how to bypass safety chceck?
  • From: "slawek" <slawek at host.pl>
  • Date: Thu, 29 Jul 2010 06:44:46 -0400 (EDT)
  • References: <i2ok3i$7ni$1@smc.vnet.net>

U=BFytkownik "Daniel Lichtblau" <danl at wolfram.com> napisa=B3 w wiadomo=B6ci grup
dyskusyjnych:i2ok3i$7ni$1 at smc.vnet.net...
> You neglected to mention what happened when you tried it. Was it
> something bad (e.g. program hang or frozen computer)?
>
> Daniel Lichtblau
> Wolfram Research


I solve sets of DDE equations.  The simplest example is:

{x1'[t]   ==   x1[t]   -   x1[t - 2 d] * x2[t - d]^2  -  2 * x1[x - d] *
x2[x - 2 d] * x2[x - d],
 x2'[t]   ==   x2[t]   -   x2[t - 2 d] * x1[t - d]^2  -  2 * x2[x - d] *
x1[x - 2 d] * x1[x - d]}

Above equations are related to integro-differential equations, which are can
not be solved non-numerically and which are nonlinear plasma physics
equations. The history function is a main trick to solve DDE, because it
extended domain of time t. (This "trick" and DDE have been never applied in
published works on the topic.)

The ODE-INT "old method" take hours to obtain a solution (Fortran), the DDE
"new method" gives a solution after about half a second (Mathematica 7, the
same PC).  Wow!

There are - and it is ok - some subdomains of the time shift d, where
solutions are chaotic. I use an "module", to generate plots and animations
(or use Slider/Dynamic):

plot[d_] := Module[{...}, NDSolve[...]; ...; Plot[...]]
plots = Table[plot[d],{d,0.05,5.0}]
ListAnimate[plots]

For d = 5.0 Mathematica refuses give a solutions and warnig is generate d. It
is ok, because the solution is chaotic. Nevertheless I would like have even
completly noisy "wrong" solution instead a blank plot. Thus the question how
to weak "quality checking" in NDSolve and to force NDSolve to always produce
an output, even if the covergence is poor.

NDSolve return when it finish computations, thus - I suppose - Infinity as
the number of steps would generate infinite computation time and no results.
I do not look for more accurate results. I look for an option to switch
NDSolve to a "dumb mode".

TIA
slawek




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