Re: [Maxima-discuss] rkf45 share

[Robert D. <rob...@gm...>]

On 2017-01-17, Dimiter Prodanov <dim...@gm...> wrote:

> I think there was a numerical issue in the package of Panagiotis
> Papasotiriou.

I'll be happy to fix the coefficients if you can be more specific about
what is the problem.

> 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])

b1 and b2 are supposed to sum to 1, right? Looks like b2 is OK but b1
doesn't sum to 1. I think it should have 2197/4104 instead of 2197/4101.

I don't know how to check the a's, maybe you can suggest something.

Also, I don't understand how these coefficients fit into the existing
rkf45.mac. I think it's best for this purpose if you'll provide a patch
that shows what lines need to be changed.

best,
Robert Dodier