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