Re: 2D recursion relation
- To: mathgroup at smc.vnet.net
- Subject: [mg42280] Re: [mg42198] 2D recursion relation
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 26 Jun 2003 05:36:30 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Good news: RSolve in version 5 can solve partial recurrence equations (well, some of them anyway). Bad news: It can't solve this particular one, which is not really surprising since the general solution requires the use of Fourier transforms. This is rather analogous to the situation with DSolve. Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/ http://platon.c.u-tokyo.ac.jp/andrzej/ On Monday, June 23, 2003, at 06:49 PM, Dr. Wolfgang Hintze wrote: > The package > > << "DiscreteMath`RSolve`" > > can solve 1-dimensional recursion relations such as the Fibonacci > sequence: > > In[6]:= > equ1D = n[t + 1] == n[t] + n[t - 1]; > > In[7]:= > RSolve[{equ1D, n[0] == n[1] == 1}, n[t], t] > > Out[7]= > {{n[t] -> (2^(-1 - t)*(-(1 - Sqrt[5])^(1 + t) + > (1 + Sqrt[5])^(1 + t)))/Sqrt[5]}} > > My question is: how can I solve 2-dimensional equations such as > > equ2D = n[x, t + 1] == n[x - 1, t] + n[x + 1, t]; > > which describes the simplest form of a 1D random walk? > > Any help is greatly appreciated. > > Wolfgang > > >