Operator exponential

First of all, thank you for developing this package, it's a very instructive way to learn about function decomposition methods!

And I do like the way time dependent PDEs can be solved by extending the state-space to include the time domain (see this example) and defining the IC as a Dirichlet BC.

1. But I was wondering if there was any discussion/plan of solving linear PDEs (u' = A*u) with the exponential of operators (u = exp(A*t)*u0) by overloading exp? Matlab's chebfun has the expm function (see examples here and here), but it seems like the operators there have BCs baked in. There is an ApproxFun example too, but it's not very intuitive as one is not applying the propagator to a Fun type directly, and you need to explicitly specify how many coefficients to use.

2. Also for more general PDEs, what is the status on using Fun in ODEProblem? I noticed that naively defining something like

function model!(du,u,p,t)
    du = F(u,p)
end

and plugging it into ODEProblem(model!,u0,tspan,p) won't work. I noticed this question has been asked before, but since it's been a few years, I was wondering if there was any progress on this front?

Thank you again!

Start by reading the linked ApproxFunExamples PDE files, especially Linear KdV.jl and Heat equation.jl, then inspect the ODEProblem(model!, u0, tspan, p) entry point and the model! example. Clarify whether the requested work is operator exponentials, Fun support in ODEProblem, or both; done requires an agreed API and corresponding working examples or tests.