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MathGroup Archive 1997

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Re: Boundary Value Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7129] Re: Boundary Value Problem
  • From: NEWSMGR at selu.edu
  • Date: Sun, 11 May 1997 02:57:26 -0400 (EDT)
  • Organization: Southeastern Louisiana University
  • Sender: owner-wri-mathgroup at wolfram.com

Relay-Version: ANU News - V6.1B9 05/16/94 VAX/VMS V6.2-1H3; site alpha.selu.edu
Subject: [mg7129] Re: Boundary Value Problem
From: Paul Abbott <paul at physics.uwa.edu.au>
To: mathgroup at smc.vnet.net
Organization: University of Western Australia

On 24 Apr 1997 05:04:15 -0400, "Rick A. Sprague" <sprague at egr.msu.edu> 
wrote:

> > I have
> > come to a problem, though, that seems to have stumped MMA.  Can the
> > following problem be solved with out writing a lengthy MMA program?
> >
> > y'''''[x]+y[x]==0
> >
> > Conditions
> > y[0]==0
> > y'[0]==7
> >
> > y[1]==1
> > y'[1]==10
> > y''[1]=5

Mathematica can solve this problem directly and exactly -- but the exact
solution is quite long and complicated.  Here is a simple way of solving
the system quasi-numerically: 

	In[1]:= Y = DSolve[y'''''[x] + y[x] == 0, y, x]//First;

	In[2]:= N[y[0] == 0 /. Y]; 

	In[3]:= N[y'[0] == 7 /. Y]; 

	In[4]:= N[y[1] == 1 /. Y]; 

	In[5]:= N[y'[1] == 10 /. Y]; 

	In[6]:= N[y''[1] == 5 /. Y]; 

	In[7]:= y[x] /. Y /. Chop[First[Solve[{%, %%, %%%, %%%%, %%%%%}, 
				Array[C, 5]]]]

	Out[7]=

                                      1/5
-191.276                          (-1)    x
-------- + (57.8964 + 9.82354 I) E          + 
    x
   E
 
                                                   3/5
  37.7414 - 127.795 I                          (-1)    x
  ------------------- + (37.7414 + 127.795 I) E          + 
           2/5
       (-1)    x
      E
 
  57.8964 - 9.82354 I
  -------------------
           4/5
       (-1)    x
      E

Cheers,
	Paul 

_________________________________________________________________ 
Paul Abbott
Department of Physics                       Phone: +61-9-380-2734 
The University of Western Australia           Fax: +61-9-380-1014
Nedlands WA  6907                         paul at physics.uwa.edu.au 
AUSTRALIA                           http://www.pd.uwa.edu.au/Paul

          God IS a weakly left-handed dice player
_________________________________________________________________


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