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MathGroup Archive 1997

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ODE boundary value problem failure with chasing method

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8006] ODE boundary value problem failure with chasing method
  • From: Kim-Ee Yeoh <key9 at universe.digex.net>
  • Date: Wed, 30 Jul 1997 23:58:00 -0400
  • Organization: DIGEX, Inc.
  • Sender: owner-wri-mathgroup at wolfram.com

Hi everyone,

I need to solve the ODE below that arises in an approximation to a plasma
transport equation.  The following is Mathematica 3.0 output:

In[12]:= 6 F[w]+(24.*(1-w)^4-10.00*(1-w)^3+(6.00*w-2.00*w^2)*(1-w))*F'[w]+
(-1.00*w*(1-w)^3+1.00*w^2*(1-w)^2-24.*(1-w)^5+4.*(1-w)^4)*F''[w]+
4.*(1-w)^6*F'''[w] == 0
 
                               3              4                       2
Out[12]= 6 F[w] + (-10. (1 - w)  + 24. (1 - w)  + (1 - w) (6. w - 2. w )) 
 
                          4              5             2  2
>      F'[w] + (4. (1 - w)  - 24. (1 - w)  + 1. (1 - w)  w ) F''[w] + 
 
                6  (3)
>     4. (1 - w)  F   [w] == 0

... (irrelevant -- deleted)
 
In[18]:= NDSolve[ {%12,F[0]==1,F'[0]==-1,F[0.999]==0},F,{w,0,0.999} ]
 
NDSolve::inaccur: 
   Now doing a transformation to the original differential equation. The
    result may be inaccurate at a low working precision.
 
NDSolve::unsol: 
   Not possible to initiate boundary value problem with the chasing method
 
                                        3              4
Out[18]= NDSolve[{6 F[w] + (-10. (1 - w)  + 24. (1 - w)  + 
 
                               2
>          (1 - w) (6. w - 2. w )) F'[w] + 
 
                   4              5             2  2
>       (4. (1 - w)  - 24. (1 - w)  + 1. (1 - w)  w ) F''[w] + 
 
                  6  (3)
>       4. (1 - w)  F   [w] == 0, F[0] == 1, F'[0] == -1, F[0.999] == 0},
F, 
 
>    {w, 0, 0.999}]
 

The solution F[w] has the obvious singularity at w=1, and therefore I used
a boundary condition at w=0.999 instead.

The implementation notes in the latest edition of the Mathematica Book I'm
using refers to a "Gel'fand-Lokutsiyevskii chasing method."  I'm loathe to
follow up on this obscure reference, as I really need to get on with my
research.  I'm now thinking of trying out some Netlib packages
instead, but I'm told there aren't really many robust packages for such
stiff two-point boundary value ODEs.

Has anyone out there encountered something similar with their boundary
value ODEs?  I'd really appreciate any advice on how to proceed from here.


Regards,
Kim-Ee Yeoh



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