Re: Default merged to stable for upcoming 4.2 release

[Marco Caliari]

On Thu, 6 Oct 2016, Schöps, Sebastian wrote:

> > 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...

ode23tb in Matlab advances with order 2

tolrange=[1e-4,1e-6,1e-8,1e-10];
counter=0;
for tol = tolrange
counter=counter+1;
options.AbsTol=tol;
options.RelTol=tol;
[t,y] = ode23tb(@(t,y) y,[0,1],1,options);
err(counter) = abs(exp(1)-y(end));
ts(counter)=length(t);
end
loglog(ts,err,'*',ts,err(end)*(ts/ts(end)).^(-2))

Marco