Re: solve this equation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg7304] Re: solve this equation?*From*: Eugene Lee <elee at aw.sgi.com>*Date*: Fri, 23 May 1997 01:41:33 -0400 (EDT)*Organization*: Alias Wavefront*Sender*: owner-wri-mathgroup at wolfram.com

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. There is no problem with my solution. Ask any mathematician if you don't see. Eugene Lee