Re: Default merged to stable for upcoming 4.2 release

[Schöps , Sebastian]

> Am 06.10.2016 um 09:29 schrieb c. <address@hidden>:
> On 6 Oct 2016, at 09:22, Marco Caliari <address@hidden> wrote:
>> 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?
> 
> we don't have ode23tb at the moment ...
> 
> but for example in odebwe and odefwe the same method with different timesteps 
> is used to estimate the error
> so also there q = oder_dt = order_interp = 1.

I think there is some confusion here. There are up to three different orders 
for (A) time stepping, (B) prediction and (C) interpolation. Typically one uses 
a higher order for prediction (with some exceptions as Richardson is used for 
bweuler) and most codes also continue time stepping with the higher order as 
Marco has quoted from Hairer's book. My perception was that the ordering odeAB 
vs. odeBA tells you with which order one continues.

We are currently doing what Matlab does, i.e., advancing with the higher order. 
Interpolation should also return ("dense output") solutions of appropriate high 
order. I think the only exception is ode78. Jacopo and I verified this 
yesterday. However, we can check this once more...

Sebastian