       Re: Nonlinear Discrete

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: Nonlinear Discrete
• From: scherm at ifm.uni-hannover.de
• Date: Fri, 25 Feb 1994 15:19:20 +0000

```Responding to :
>Dear Users
>	I am currently engaged in writing a function to deal with
>some discrete nonlinear system, but unfortunately I am a completely novice
>as Mathematica programmer.  Can someone out there give some clue how
>to implement a problem such as the following one, please?
>	y(t)=a*y(t-1)+b*y(t-2)+c*y(t-1)*y(t-1) ->  First how to code?
~~~~~~~~~~~~~~~~~~

First you specify the difference equation like

y[k_]:=0.5*y[k-1]+1*y[k-2]+y[k-1]*y[k-1];

Then you determine the series y(k) with two initial values

y=1;
y=1;

All you have to do now is to 'enjoy' the results:

Print[y,"  ",y,"  ",y,"  ",y];

gives
60
2.5  8.5  79.  5.99223 10

This method is quite simple but
be aware that you defined a recursive difference equation. The MATHEMATICA
Kernel will need a long time to calculate for example y(9).
If you are interested in getting the complete sequence
y(0)..y(9) it will be better to use the following

y=1;
y=1;

For[i=2,i<=9,i++,
y[i]=0.5*y[i-1]+1*y[i-2]+y[i-1]*y[i-1];
Print[y[i]];
];

It will run much faster and gives:
2.5
8.5
79.
6289.
7
3.95547 10
15
1.56458 10
30
2.4479 10
60
5.99223 10

(Norbert Scherm)

>
>
>

```

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