odefun

[Gert Van den Eynde]

hi,

I'm a complete newbie to mpmath. For a project, I would like to solve a set of ODEs (mildly stiff) using the taylor method (for high accuracy) and I have a couple of questions regarding the current implementation of odefun and ode_taylor. I would like to state some observations, please correct me if I misunderstood something.

* there is no means for the user to provide the high-order derivatives of the RHS

* these derivatives are calculated numerically, but not using the mpmath.diffs method

* there is at the moment no link with automatic differentiation tools

* the degree (or order) is fixed, either by the user either by a heuristic at the start of integration. It is not varied during the solver process.

* according to github, there has been no update on the calculus part of mpmath for 9 months. Please, don't see this as criticism, I just would like to know if someone is still working on this and what she/he is doing.

Thanks,
Gert

[Fredrik Johansson]

Hello Gert,

Sorry for the late reply. I've been on vacation and let my inbox pile up.

On Fri, Aug 17, 2012 at 4:26 PM, Gert Van den Eynde <gvde...@gmail.com> wrote:
> hi,
>
> I'm a complete newbie to mpmath. For a project, I would like to solve a set of ODEs (mildly stiff) using the taylor method (for high accuracy) and I have a couple of questions regarding the current implementation of odefun and ode_taylor. I would like to state some observations, please correct me if I misunderstood something.
>
> * there is no means for the user to provide the high-order derivatives of the RHS

To solve a high-order system, you have to rewrite it as a first-order
matrix system (the way most ODE solvers work).

> * these derivatives are calculated numerically, but not using the mpmath.diffs method

Correct. The code basically does the same thing as mpmath.diffs.

> * there is at the moment no link with automatic differentiation tools

Correct.

> * the degree (or order) is fixed, either by the user either by a heuristic at the start of integration. It is not varied during the solver process.

Correct. The error control in odefun is very much naive.

> * according to github, there has been no update on the calculus part of mpmath for 9 months. Please, don't see this as criticism, I just would like to know if someone is still working on this and what she/he is doing.

I'm not aware of anyone working actively on it. I would like to have
more functions for ODEs and analytic continuation, and better
numerical integration code, but I'm focusing on other things right now
and don't know when I will get back to working on mpmath.

By the way, there is a project by Jorn Baayen called pytaylor
(http://gitorious.org/pytaylor) that implements some more advanced ODE
solvers using SymPy and mpmath. Perhaps some of it could be useful to
you. It has not been updated since 2009, however.

Fredrik