Re: Default merged to stable for upcoming 4.2 release

[Marco Caliari]

On Thu, 6 Oct 2016, c. wrote:

> On 6 Oct 2016, at 09:06, Marco Caliari <address@hidden> wrote:
>
> > 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
>
> mmmh ...
>
> so the 'order' that we're using for interpolation an the order used for 
> timestep selection are different,
> so shall we just use order instead of order + 1 in the formula? Would that 
> apply to all methods? I think we may have
> problems for those integrators that use Richardson approach to estimeta 
> truncation error ...
>
> should we use two variables order_dt and order_interp instead? what do you 
> suggest?

This is the most flexible. What is the current strategy for, say, ode23tb? 
This function uses the embedded method of order three for the estimates, 
but the method of order two for advancing in time. In this case, q = 
oder_dt = order_interp = 2. Right?

Marco