plotdf questions: tstep, Runge-Kutta and singular points

Hi,
?'m sorry that the documentation is outdated. The adaptive step 
Runge-Kutta method is now used always and  therefore, the tstep value is 
ignored; the value of tstep will changed in order to keep steps with a fixed
length in the phase plane. That method introduces the instabilities that 
you have seen near the equilibrium points; I have some ideas to improve 
that behavior in future versions, but in the meantime I suggest that
you try using the option direction -> forward (either add 
[direction,forward] in the plotdf command, or changing
it in the menu); that way the trajectories will not move back to the 
equilibrium point. You can also try changing
the value of nsteps.
Regards,
Jaime


On 04/18/2013 05:46 PM, Ilya Schurov wrote:
> Hi there,
>
> I have some problems with plotdf command. I'd like to plot some nice
> phase portraits of singular points. However, it seems that integration
> algorithm becomes inaccurate near singular points (e.g. nodes).
>
> Here is an example.
>
> plotdf([x**2-y,log(1-x+x**2)-log(3)],[x,1,3],[y,3,5]);
>
> The output looks like this:
>
> http://schurov.com/maximassode.png
>
> One can see artifacts near the singular point.
>
> I tried to overcome this issue by setting tstep parameter as described
> in the docs (http://maxima.sourceforge.net/docs/manual/de/maxima_66.html).
> However, it seems that the system simply ignores tstep parameter. At
> least, I tried commands
>
> plotdf([x**2-y,log(1-x+x**2)-log(3)],[x,1,3],[y,3,5],[tstep,100000]);
>
> and
>
> plotdf([x**2-y,log(1-x+x**2)-log(3)],[x,1,3],[y,3,5],[tstep,0.000001]);
>
> I believe that the first command should give very inaccurate picture,
> and the second one have to produce much more accurate pictures. In
> fact, they are identical to each other. Note also, that I do not have
> "tstep" parameter in the "Plot setup" window.
>
> The other idea was to switch to Runge-Kutta method. The docs says it's
> possible ("The Adams Moulton method is used for the integration; it is
> also possible to switch to an adaptive Runge-Kutta 4th order method"),
> but I didn't found such an option in the options list.
>
> Version of my Maxima:
>
> Maxima 5.29.1 http://maxima.sourceforge.net
> using Lisp SBCL 1.0.55.0.debian
>
> Any ideas?
>
> --
> With best regards,
> Ilya V. Schurov.
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