<div class="gmail_quote">On Wed, Oct 19, 2011 at 16:08, 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>I get it now... My confusion was due to being used to derived all scheme on the pde, then discretizing, whereas the documentation assumes that the equation is already discretized. I should have figured it out. </div>
</blockquote><div><br></div><div>For software purposes and sometimes also for analysis, the "method of lines" approach is often useful. That's how the TS interfaces are set up.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div><br></div><div>Is it right to think of the division between ODE, DAE and IMEX in the documentation as Fully Explicit vs. Fully implicit vs. Semi-implicit?</div></blockquote></div><br><div>Sure, but it's a matter of the interface more than the method. You can write</div>
<div><br></div><div>Xdot = F(X)</div><div><br></div><div>and use -ts_type beuler to solve it fully implicitly. I would consider</div><div><br></div><div>G(X,Xdot) = F(X)</div><div><br></div><div>to be the most general interface. When an IMEX method is used, this has the clear semantics that G is implicit and F is explicit. Explicit methods usually assume G(X,Xdot) = Xdot which is the default if you never call TSSetIFunction. I think we will eventually have support for using standard explicit methods where you just put the mass matrix into G, but that isn't done yet.</div>