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Re: solve this equation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6928] Re: solve this equation?
  • From: Eugene Lee <elee at aw.sgi.com>
  • Date: Tue, 29 Apr 1997 20:48:10 -0400 (EDT)
  • Organization: Alias Wavefront
  • Sender: owner-wri-mathgroup at 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.

Eugene


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