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Re: Graphing Difference Equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91415] Re: Graphing Difference Equation
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 21 Aug 2008 04:13:53 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g8gj3h$eso$1@smc.vnet.net>

Walkman wrote:

> I have a trouble in graphing differece equation using mathematica.
> 
> For instance, I get a difference equation,
> 
> y_{t} = 1.5y_{t-1} - .5y_{t-2} = 0
> 
> Since I don't know how to input the code for graphics and just want
> 
> to check how the graph looks like,
> 
> I input the solution instead, A(-1.2)^t + B(.5)^t where A and B
> 
> constants
> 
> For simplicity, I choose A = B = 1.
> 
> Plot[(-1.2)^t + (.5)^t,{t,0,20}]
> 
> The problem is that it doesn't work at all.
> 
> If anyone who know exact way to graph difference equation, plz
> 
> tell me.

The plotting function *ListPlot* [1], combined with *Table* [2], should 
generate the desired graph. For instance,

   In[1]:= pts = Table[{t, (-1.2)^t + (.5)^t}, {t, 0, 20}]
           ListPlot[pts, Filling -> Axis]

   Out[1]= {{0, 2}, {1, -0.7}, {2, 1.69}, {3, -1.603}, {4,
     2.1361}, {5, -2.45707}, {6, 3.00161}, {7, -3.57537}, {8,
     4.30372}, {9, -5.15783}, {10, 6.19271}, {11, -7.4296}, {12,
     8.91634}, {13, -10.6992}, {14, 12.8392}, {15, -15.407}, {16,
     18.4884}, {17, -22.1861}, {18, 26.6233}, {19, -31.948}, {20,
     38.3376}}

   Out[2]= [... graphic displayed w/ points above & below the x-axis ...]


Also, note that difference equations can be solved with *RSolve* [3].

Regards,
-- Jean-Marc

[1] http://reference.wolfram.com/mathematica/ref/ListPlot.html

[2] http://reference.wolfram.com/mathematica/ref/Table.html

[3] http://reference.wolfram.com/mathematica/ref/RSolve.html


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