using Sympy for solving PDAEs as taylor series?

[foadsf]

I posted this question here on Reddit and I was advised to repost here as well:

Mathematica has this nice function of AsymptoticDSolveValue which can take an ODE plus the initial conditions and then return a power series approximation of the solution. I was wondering if there is anything like that for solving Partial differential algebraic equation in Python-SymPy or other Python symbolic libraries? If not how can we write such a functions? If I get the algorithm I might be able to implement it myself.

[Kalevi Suominen]

I don't think there is anything like that in SymPy. It looks like you are expecting to solve a Cauchy initial value problem for partial differential equations. By the Cauchy-Kowalevski theorem, that is possible for equations with analytic coefficients. For the algorithm, you should look into the proof of the theorem.

Kalevi Suominen

[foadsf]

I'm following this idea here