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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