[Octave-bug-tracker] [bug #50012] ode23 internal interpolation

[Jacopo Corno]

Follow-up Comment #3, bug #50012 (project octave):

Hi,

I do not believe this issue is related to the "Refine" bug.

The error seems indeed to be in the interpolation routine. As Carlo mentioned
the choice in Matlab is not clear. What is stated in the documentation is:

"... the solutions produced at the specified points are of the same order of
accuracy as the solutions computed at each internal step"

Tests show that ode23 is a third order scheme in Matlab (i.e. it uses local
extrapolation) so in Octave we set the order of the solver to 3 and that order
is used to choose the proper interpolation algorithm. In this case it is a
cubic hermite interpolant that exploits the values and the derivatives at t
and t+dt. There could be a bug there, I will check...

In the case of ode45, although it is a scheme of order 5 (it uses local
extrapolation too), Shampine proposes to use a 4th order interpolation scheme
that avoids further function evaluations. I am not sure what method Matlab is
choosing in the end.

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