       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?  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:= eqns // InputForm
> Out//InputForm= {u[x] == u[-1 + x]/2 + u[1 + x]/2, u == 1, u[-4]
> == 0}
>
> In:= RSolve[eqns, u[x], x]
>                   If[x >= -3, 4 + x, 0]
> Out= {{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