Re: [Maxima-discuss] rkf45 share

[Eric B. <ej...@gm...>]

What  errors have you observed with rkf45?

I've been looking tonight at the rkf45.mac in my installation.
I believe the coefficients implemented there are all correct---agreeing
with the well-known rkf45 values Dimiter quotes.  One tiny error though  in
the values quoted above for b1:  I think it should be 2197/4104, not
2197/4101.


Here's one ref to the method:
http://pauli.uni-muenster.de/tp/fileadmin/lehre/NumMethoden/SoSe10/Skript/RKM.pdf

Another ref is wikipedia!
https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta%E2%80%93Fehlberg_method


That said, here's an online ref that has the 2197/4101 value
http://maths.cnam.fr/IMG/pdf/RungeKuttaFehlbergProof.pdf

 I note that changing that one value (used to estimate the error at each
step) from 2197/4104 to 2917/4101 breaks the rkf45 as implemented.

Eric

On Tue, Jan 17, 2017 at 9:11 PM Robert Dodier <rob...@gm...>
wrote:

> On 2017-01-17, Dimiter Prodanov <dim...@gm...> wrote:
>
> > a2:float([ 1/4,  1/4]), /* 2^2 */
> > a3:float([ 3/8, 3/32, 9/32]), /* 2^5 */
> > a4:float([ 12/13, 1932/2197, -7200/2197, 7296/2197]),  /* 13^3 */
> > a5:float([ 1, 439/216, -8, 3680/513, -845/4104]),
> > a6:float([ 1/2, -8/27, 2, -3544/2565, 1859/4104, -11/40]),
> > b1:float([ 25/216, 1408/2565, 2197/4101, -1/5]),
> > b2:float([ 16/135, 6656/12825, 28561/56430, -9/50, 2/55])
>
> I don't doubt you, but it would help a lot if you could give a reference
> (a book, web page, or other publicatiuon) for these. Do they satisfy a
> relation that can be verified? If so you cculd put that in a comment.
>
> Also as a practical matter it is easier to handle a request of this kind
> if you provide a diff instead of only the new text.
>
> best
>
> Robert Dodier
>
>
>
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