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Re: Interesting problem

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On 31/05/16 09:27, alsor@interia.pl wrote:
> W dniu niedziela, 29 maja 2016 23:01:07 UTC+2 użytkownik HGWilson, DSc. napisał:
>> On 30/05/16 03:35, alsor@interia.pl wrote:
>>> W dniu niedziela, 29 maja 2016 01:35:27 UTC+2 użytkownik HGWilson, DSc. napisał:
>>>
>>>> I actually create ellipses by iterating Newton's force equation and they
>>>> are sufficiently accurate over one orbit for brightness curve
>>>> simulation. (using about 40000 points) The operation takes a fraction of
>>>> a second on a pretty fast PC. Over many cycles, the generated orbit
>>>> naturally precesses, which made me wonder if the integration 'error' is
>>>> actually simulating the finite speed of gravity, which in turn could
>>>> conceivably be a contributing factor in planetary precession.
>>>
>>> Yes. The problem with the artificially generated precession,
>>> during numerical integration is well known... for the experts of the numerics methods.
>>>
>>> This artifical precession goes backward usually,
>>> thus it decreases the real precession... in the many-body problem simulaion.
>>
>> Is there a way to correct the error?
>>
>> In the x direction, the simplest iteration for each time unit uses
>> v=v+a: x=x+v: a= fn(x), (same for y), repeat
>>
>> That can generate quite accurate ellipses.....but the ends do not quite
>> match. Is it possible to make an exact correction so they will?
>
> There are some special methods to reduce this 'numerical' precession..
> for example the force-gradient metods.
> http://arxiv.org/pdf/1602.01049.pdf
>

>        }
>
>       forceg(a, y, sqr(h)/12); // g + h^2/48 grad(g^2); grad g^2 = 4 g^2 ...
>       //   v2 = v1 + a*h 2/3; r1 = r1 + v2 h/2;
>       for(int i = 0; i < nB; i++)
>        {
>           y[i].v.addm(a[i], h*(2.0/3));
>           y[i].r.addm(y[i].v, h2);
>        }
>
>       force(a,y,nB);
>       for(int i = 0; i < nB; i++)
>        {
>           y[i].v.addm(a[i], h6);
>        }
> }

I think there might be an easier and more straightforward way using 
computers but it might be a bit slower. Knowing the final error after 
one cycle, it should be possible to empirically correct each step until 
the error disappears.

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Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-26 07:05 +1000
  Re: Interesting problem Poutnik <poutnik4nntp@gmail.com> - 2016-05-25 23:17 +0200
    Re: Interesting problem "David (Time Lord) Fuller" <fuller.david@hotmail.com> - 2016-05-25 14:20 -0700
  Re: Interesting problem "David (Time Lord) Fuller" <fuller.david@hotmail.com> - 2016-05-25 14:18 -0700
  Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-25 16:20 -0500
    Re: Interesting problem Tom Roberts <tjroberts137@sbcglobal.net> - 2016-05-25 18:31 -0500
    Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-27 03:25 +1000
      Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-26 13:32 -0500
        Re: Interesting problem HGW <hw@...> - 2016-05-27 12:15 +1000
          Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-27 04:26 -0500
            Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-27 19:52 +1000
              Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-27 05:46 -0500
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-27 21:55 +1000
                Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-27 07:23 -0500
                Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-27 07:26 -0500
                Re: Interesting problem "David (Time Lord) Fuller" <fuller.david@hotmail.com> - 2016-05-27 05:29 -0700
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-28 19:47 +1000
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-05-28 04:12 -0700
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-05-28 04:51 -0700
                Re: Interesting problem alsor@interia.pl - 2016-05-28 11:27 -0700
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-05-28 14:01 -0700
                Re: Interesting problem alsor@interia.pl - 2016-05-28 15:10 -0700
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-29 09:35 +1000
                Re: Interesting problem alsor@interia.pl - 2016-05-29 10:35 -0700
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-30 07:01 +1000
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-05-29 15:22 -0700
                Re: Interesting problem alsor@interia.pl - 2016-05-30 13:05 -0700
                Re: Interesting problem alsor@interia.pl - 2016-05-30 16:27 -0700
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-31 20:56 +1000
                Re: Interesting problem alsor@interia.pl - 2016-05-31 08:40 -0700
                Re: Interesting problem HGW <hw@...> - 2016-06-02 09:40 +1000
                Re: Interesting problem alsor@interia.pl - 2016-06-02 11:53 -0700
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-05-31 04:25 -0700
                Re: Interesting problem mlwozniak@wp.pl - 2016-05-31 04:58 -0700
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-06-01 06:31 +1000
                Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-31 16:30 -0500
                Re: Interesting problem HGW <hw@...> - 2016-06-02 09:44 +1000
                Re: Interesting problem JanPB <filmart@gmail.com> - 2016-05-31 14:58 -0700
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-06-01 06:24 +1000
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-06-01 06:23 -0700
                Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-06-01 11:11 -0500
                Re: Interesting problem HGW <hw@...> - 2016-06-02 09:47 +1000
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-06-01 18:50 -0700
                Re: Interesting problem alsor@interia.pl - 2016-06-02 12:07 -0700
                Re: Interesting problem alsor@interia.pl - 2016-06-01 08:59 -0700
                Re: Interesting problem HGW <hw@...> - 2016-06-02 10:09 +1000
                Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-29 13:52 -0500
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-30 07:09 +1000
                Re: Interesting problem Sam Wormley <swormley1@gmail.com> - 2016-05-29 16:26 -0500
                Re: Interesting problem Fabian Russell <fb@zen.info> - 2016-05-30 04:25 +0000
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-31 21:00 +1000
                Re: Interesting problem Fabian Russell <fb@zen.info> - 2016-05-31 22:46 +0000
                Re: Interesting problem HGW <hw@...> - 2016-06-02 09:32 +1000
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-05-27 05:34 -0700
                Re: Interesting problem "David (Time Lord) Fuller" <fuller.david@hotmail.com> - 2016-05-27 05:40 -0700
                Re: Interesting problem "David (Time Lord) Fuller" <fuller.david@hotmail.com> - 2016-05-27 05:43 -0700
                Re: Interesting problem rotchm <rotchm@gmail.com> - 2016-05-27 06:40 -0700
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-05-27 07:42 -0700
                Re: Interesting problem rotchm <rotchm@gmail.com> - 2016-05-27 06:36 -0700
                Re: Interesting problem Odd Bodkin <bodkinodd@gmail.com> - 2016-05-27 09:01 -0500
                Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-28 20:04 +1000
                Re: Interesting problem Prokaryotic Caspase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2016-05-28 04:34 -0700
    Re: Interesting problem Fabian Russell <fb@zen.info> - 2016-05-27 22:03 +0000
      Re: Interesting problem "HGWilson, DSc." <hgw@....> - 2016-05-28 20:10 +1000

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