2D recursion relation
- To: mathgroup at smc.vnet.net
- Subject: [mg42198] 2D recursion relation
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Mon, 23 Jun 2003 05:49:39 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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