I like SymPy, but I have been running into issues with it when I solve partial differential equations. I've constructed a toy example:
from sympy import Function, Eq
from sympy.solvers import pdsolve
from sympy.abc import x, y, t
f = Function('f')
u = f(x,y,t)
ux = u.diff(x)
uy = u.diff(y)
eq = Eq(1 + (2 * (ux/u)) + (3 * (uy/u)), 0)
print(pdsolve(eq))
Which raises an error that tells me there does not exist an implementation for two variables.
NotImplementedError: Right now only partial differential equations of two variables are supported
Often systems of PDEs are only solvable with numerical methods, which packages like py-pde are helpful for approximating, but there are techniques that can be applied to various families of PDE's.
Is there a Python package that allows for systems solving systems of partial differential equations with multiple variables symbolically?
