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From: | Marco Caliari |
Subject: | Re: GSoC ode15s |
Date: | Mon, 14 Mar 2016 10:58:17 +0100 (CET) |
User-agent: | Alpine 2.10 (DEB 1266 2009-07-14) |
On Sun, 13 Mar 2016, Carlo De Falco wrote:
On 11 Mar 2016, at 19:51, Chiara Segala <address@hidden> wrote:As another project idea I would like to work on Exponential Integrators. It could be an idea to implement, for example, the Exponential Euler and Rosenbrock methods. But I don't know if it can be an interesting proposal since these functions are not well defined even in Matlab.Chira, I lke this project proposal, I would be interested in mentoring (or rather co-mentoring) on it. As you also stated I think it should have lower priority with implementation of ode15s, because it is not a functionality for which there as much demand. Definitely an implementation of this feature should go iinto odepkg and not in core-Octave. That said, I do encourage you to submit an application for GSOC about this. The first point to investigate before starting development would be what is the state of algorithms for computing matrix exponential in Octave and how that compares to Matlab. I know there is another project being considered about matrix functions and I am not fully aware of its state of advancement but I have seen that discussed on the list recently, I suggest you look at those discussion threads.
Dear Chiara,I like too your idea on exponential integrators and I would be available as co-mentor. About the other project on matrix functions, it would be completely different. In fact, in exponential integrators it is required only the action of the matrix exponential to a vector. To this purpose, one of the best (fast, reliable) methods available is the one developed by Nick Higham (Computing the action of the matrix exponential with an application to exponential integrators). He very recently made his code available with a free license
https://github.com/higham/expmvOf course, this is just a small ingredient of an exponential integrators package. Anyway, I'm pretty sure it does not work in Octave as is. Can you please verify and fix it (or report what does not work and why)?
Moreover, the two methods you mentioned (exp. Euler and exp. Rosenbrock-Euler) are very basic methods with no adaptive time step. Can you find the relevant references for exponential integrators?
Best regards, Marco
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