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[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. > > 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[5]:= eqns // InputForm > Out[5]//InputForm= {u[x] == u[-1 + x]/2 + u[1 + x]/2, u[4] == 1, u[-4] > == 0} > > In[6]:= RSolve[eqns, u[x], x] > If[x >= -3, 4 + x, 0] > Out[6]= {{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