On Mar 22, 3:55 am, Fredrik Johansson <fredrik.johans...@gmail.com>
wrote:
>This is a great project; I hope this gets accepted.
Does sympy review the applications relating to it directly, or does
python choose for it. Perhaps I should go introduce myself on the
python-gsoc mailing list.
> * Implement the (generalized) hypergeometric differential equation and
> add hypergeometric functions like Bessel and Airy functions to SymPy
> (these functions are needed to solve many important ODEs from physics
> and elsewhere)
We haven't learned about these yet (remember that I am presently only
half way through the semester in my ODE's class), but from what I can
tell, they involve series solutions. I only have three months to do
this. If I have time to do series, then I will go ahead and to it,
but for my applications, I think it might hurt it if I make my project
impossible. One of the nice things about implementing ODEs is that I
can shoot for a realistic goal and if I achieve it faster than I
thought I would, then I could easily logically continue the project
from there by implementing more advanced types of solutions, i.e.,
series, numerical, systems of ODEs, etc.
> * Identification of singular points of linear ODEs. Series expansions
> for linear ODEs with unknown solution (see for example "Advanced
> Mathematical Methods for Scientists and Engineers" by Bender &
> Orszag). Possibly difficult, especially since the series code in SymPy
> has some problems.
I also haven't learned about this yet, but the same if it involves
series.
> * Symbolic FEM code, e.g. for approximating ODE solutions by
> polynomials (see
> e.g.http://fredrik-j.blogspot.com/2009/02/galerkins-method-in-sympy.html),
> or by trigonometric polynomials (Fourier series).
See above.
> * Implement automatic transformation of high-order ODEs to systems of
> first-order ODEs. Write wrappers for numerical ODE solvers in mpmath
> and/or SciPy so that numerical solutions can be obtained conveniently
> in SymPy.
Writing wrappers might no be as difficult. Is there already a
standard for wrappers in sympy?
> Though I will not be mentoring, I will be happy to provide guidance
> about any of the above if necessary.
I see from your blog that you participated in gsoc last year. Do you
perhaps have any advice for me, especially with regards to the
application process?
> Fredrik
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