Re: Default merged to stable for upcoming 4.2 release

[Marco Caliari]

On Thu, 6 Oct 2016, c. wrote:

> On 6 Oct 2016, at 08:39, Marco Caliari <address@hidden> wrote:
>
> > There is another point, which I supposed was in the bug tracker, but that I 
> > cannot find: in integrate_adaptive, the new dt uses (order + 1). In this case, 
> > order should be the order of the embedded method with lowest order. But it is 5 
> > in ode45, and 3 in ode23. Am I wrong, or should it be fixed?
>
> I'm not sure about this one, for compatibility with Matlab we are using the 
> highest order embedded method to compute the solution, so do we still need to 
> use the lowest order for estimating the timestep?
> c.

This is what I understand from [Hairer, Norsett, Wanner, Solving ODEs I, 
p. 168]. In particular:

q = min(p,\hat p)
h_opt = h * (1/err) ^ (1/(q+1))
"But isn't it more natural to continue the integration with the higher 
order approximation? Then the concept of "error estimation" is abandoned 
and the difference y_1-\hat y_1 is only used for the purpose of step size 
selection."

Marco