integrating a stateful function with rk()


Thank you.? I will take a look at version 5.30.? What does "post" mean?



________________________________
 From: Jaime Villate <villate at fe.up.pt>
To: Ether Jones <maxima at etherjones.us> 
Cc: maxima <maxima at math.utexas.edu> 
Sent: Wednesday, September 18, 2013 12:30 PM
Subject: Re: [Maxima] integrating a stateful with rk()
 


Hi,
do you consider this answer below the right answer?

Maxima branch_5_30_base_103_g0860c83_dirty http://maxima.sourceforge.net
using Lisp SBCL 1.1.1.0.debian
(%i1) fpprintprec:12$
(%i2) r:0$
(%i3) f(x):=(if r<5 then r:r+1, r)$
(%i4) rk('(f(x)),x,0,[t,0,1,0.2]);
(%o4) [[0.0, 0.0], [0.2, 0.5], [0.4, 1.5], [0.6, 2.5], [0.8, 3.5],
      [1.0, 4.5]]

Notice that I'm using Maxima 5.30post. In Maxima 5.27 rk() was not
      able to handle the kind of thing that you want to do. And notice
      also that you do not have to load dynamics (it will be loaded
      automatically the first time you use rk). Please update your
      version of Maxima, or you you cannot do that, locate the diretory
      share/dynamics in your system and replace the files dynamics.mac
      and complex-dynamics.lisp in that directory with their newest
      versions from the Maxima Git repository.

In any case, did you expect f(x) to have the values 1, 2, 3, 4, 5
      and 5 at the points 0, 0.2, 0.4, 0.6, 0.8 and 1?
It will not work that way because at each step rk will calculate
      f(x) for times. Different implementations of the same 4th order
      Runge-Kutta algorithm will give different results for your f(x)
      function. For example, if for some reason the algorithm calculated
      f(x) more than 4 times at one step (perhaps to check for the
      expected error of the result?) your f(x) function would become
      equal to 5 before you expected.

Regards,
Jaime

On 18-09-2013 14:49, Ether Jones wrote:


>
>
>
>What is the proper method in Maxima to integrate a stateful function with rk()?
>
>
>Below is a greatly simplified example to illustrate the problem. %i4 gives the wrong answer, and %i5 crashes.
>
>
>
>Thank you.
>
>
>
>------------------ begin example -----------------------------
>
>
>Maxima 5.27.0 http://maxima.sourceforge.net
>using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
>Distributed under the GNU Public License. See the file
          COPYING.
>Dedicated to the memory of William Schelter.
>The function bug_report() provides bug reporting information.
>
>(%i1) load("dynamics")$
>
>(%i2) r:0$
>
>(%i3) f(x):=(if r<5 then r:r+1, r)$
>
>(%i4) rk(f(x),x,0,[t,0,1,0.2]);
>
>(%o4) [[0, 0], [0.2, 0.2], [0.4, 0.4], [0.6, 0.6], [0.8, 0.8],
          [1.0, 1.0]]
>
>(%i5) rk('(f(x)),x,0,[t,0,1,0.2]);
>
>Expecting a number when the initial state is replaced in the
          equations, but instead found:
>?r
>#0: rk(odes=f(x),state=x,initial=0,domain=[t,0,1,0.2])
>?-- an error. To debug this try: debugmode(true);
>
>
>-------------------- end --------------------------------------
>
>