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MathGroup Archive 1997

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Re: Re: solve this equation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7305] Re: [mg7200] Re: solve this equation?
  • From: Eugene Lee <elee at aw.sgi.com>
  • Date: Fri, 23 May 1997 01:41:34 -0400 (EDT)
  • Organization: Alias Wavefront
  • Sender: owner-wri-mathgroup at wolfram.com

Daniel Lichtblau wrote:
> 
> Wilson Figueroa wrote:
> >
> > There is a problem with your solution.
> >
> > Check the basic math once more.
> >
> > Eugene Lee <elee at aw.sgi.com> wrote in article
> > <5k6g77$5bf$1 at dragonfly.wolfram.com>...
> > > Hong-liang Xie wrote:
> > > >
> > > > Can Mathematica be used to handle equations as follows:
> > > >
> > > >          u[x]  = 0.5 u[x-1] + 0.5 u[x+1]
> > > >          u[ 4] = 1
> > > >          u[-4] = 0
> > > >
> > > > and find result for, say, u[0]?  Note that transforming
> > > > the equation to
> > > >
> > > >          2u[x+1] = u[x]  - u[x-1]
> > > >
> > > > doesn't help since the initial conditions are given on
> > > > the points 4 and -4.
> > > >
> > > > Any hint would be appreciated.  Thanks a lot!
> > > >
> > > > Hong
> > >
> > > You don't need Mathematica at all. The equation
> > >         u[x]  = 0.5 u[x-1] + 0.5 u[x+1]
> > > is satisfied by any linear function (ie, whose graph is a straight
> > > line). The boungary conditions then fix the line, giving the solution as
> > >         u[x]=(x+4)/8
> > >
> > > By the way, your transformed equation is written incorrectly.
> 
> I tried this in our development version of Mathematica using the
> recurrence-solver RSolve (in the standard add-on package
> DiscreteMath`RSolve`). I rationalized the coefficients because this sort
> of code is difficult to make work in conjunction with approximate
> numbers.
> 
> In[5]:= eqns // InputForm
> Out[5]//InputForm= {u[x] == u[-1 + x]/2 + u[1 + x]/2, u[4] == 1, u[-4]
> == 0}
> 
> In[6]:= RSolve[eqns, u[x], x]
>                   If[x >= -3, 4 + x, 0]
> Out[6]= {{u[x] -> ---------------------}}
>                             8
> 
> Daniel Lichtblau
> Wolfram Research
> danl at wolfram.com

I have replied to Daniel via email, but to whoever being confused by
this trivial problem, let me repeat:

1) There is no problem with my solution;

2) There is a problem with the Mathematica solution Daniel got.

Eugene Lee


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