Time convolutions

[isaacbasil]

Description

For some of the models I'm working with it would be interesting to have a time convolution operator,
$\int_{0}^{t}f\left(\tau\right)g\left(t-\tau\right)d\tau$,
where $f(t)$ would be some known function that is a pybamm.Interpolant class, and $g(t)$ would be an unknown function that is being solved for in the model.
Would this be a difficult feature to implement? I was thinking it could use Scipy's convolve function, for example.

Motivation

It supports programming some models derived using volume averaging (paper coming soon!).

Possible Implementation

No response

Additional context

No response

[MarcBerliner]

This would take a lot of effort to implement because any $$\tau > 0$$ changes the class of differential equations to a system of delay differential equations/delay differential-algebraic equations, which requires a new class of solvers

[isaacbasil]

Ok no worries, thanks for your response