<div class="gmail_quote">On Wed, Oct 19, 2011 at 21:39, Blaise Bourdin <span dir="ltr"><<a href="mailto:bourdin@lsu.edu">bourdin@lsu.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div>OK, this is clear. It will be really nice indeed when everything is reorganized this way. </div><div></div></blockquote></div><br><div>Note that most methods work this way already. The main hole right now is that explicit methods don't support nontrivial mass matrices. The best error control is currently in the Rosenbrock-W methods (TSROSW), but the other methods will also grow support (via extrapolation for those methods that don't have any embedded error estimators).</div>
<div><br></div><div>One aspect that we haven't settled on an API for is user-provided stability requirements (especially for explicit methods or for the explicit part of an IMEX scheme, sometimes strong stability). Often the user can cheaply characterize some extreme eigenvalues of their system in which case we could use those estimates to limit step size instead of needing to reject steps only after the error estimator decides the accuracy is unacceptable.</div>
<div><br></div><div>Specifically, the user-provided stability limits are sharper and don't require tuning the tolerances on the time integrator so that it detects instability immediately, but does not shorten the steps excessively.</div>