Hi all,
I've written a roadmap for rewriting the ODE systems code:
https://github.com/sympy/sympy/wiki/ODE-Systems-roadmap
The roadmap represents a bonfire of the existing code and proposes to
delete all 33 of the current systems solvers. Around 7 of those are
untested and entirely broken and would be removed. The remaining 26
would be replaced by 4-5 more general (and less buggy) solvers. This
would greatly simplify the code for systems of ODEs at the same time
as dramatically increasing its capabilities.
There are 23 solvers for linear systems of ODEs and the roadmap
proposes to delete 3 broken ones and replace the other 20 with 3-4
solvers for the following cases:
Constant coefficient homogeneous (vector X and matrix A):
X' = A X
Constant coefficient nonhomogeneous (vector f):
X' = A X + f(t)
Non-constant homo/nonhomo where A(t) commutes with antiderivative B(t):
X' = A(t) X + f(t)
There should also be code to reduce higher order systems to 1st order
form (reduce to the cases above) and to partition systems of ODEs into
weakly and strongly connected components.
Most of the 10 nonlinear systems solvers are broken. Those that work
mostly come under the 2-equations autonomous class
x' = f(x, y)
y' = g(x, y)
where the solution is found from dx/dy = f/g so there should be a
solver for that case.
The work described would make an excellent GSOC project for anyone
interested. It corresponds to this idea on the GSOC ideas page:
https://github.com/sympy/sympy/wiki/GSoC-2020-Ideas#systems-of-ordinary-differential-equations
Whether this gets taken up as a GSOC project or not I hope that the
roadmap will help contributors thinking about improvements to sympy's
ODE capabilities. Most contributors looking to work on ODEs in sympy
seem to focus on improvements in the single ODE case. Those are very
useful but right now the systems code needs improvements in capability
more than the single ODE code does. There are easy wins for systems
that would make sympy's ODE handling much more useful in practical
problems.
Any feedback on the roadmap is appreciated. It is part of the wiki so
anyone can edit it (do you need push access to edit the wiki?).
Oscar
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