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Linear operators for discretizations of differential equations and scientific machine learning (SciML)

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This pull request changes the compat entry for the `LazyBandedMatrices` package from `0.5, 0.6, 0.7` to `0.5, 0.6, 0.7, 0.8`. This keeps the compat entries for earlier versions. Note: I...

It no longer (and hasn't for a long time) been about defining a DiffEqOperators interface. It's a package for finite difference discretizations of PDEs. What's a good name? Could be...

help wanted
easy

`opnorm` is left uninitialized here: https://github.com/SciML/DiffEqOperators.jl/blob/4b1bd632f717aee8be6f26601b37322f11f6b94a/src/jacvec_operators.jl#L24-L33 Another instance of JuliaLang/julia#24943

[Summation By Parts](https://en.wikipedia.org/wiki/Summation_by_parts) is the discrete equivalent of integrating by parts. This is in many cases a very convenient property to have in a discretization operator. Technically, one needs to...

I'm trying to pad my vector **u** using the boundary condition operator **Q**. It works fine for 1d data, but gives me incorrect padded vector for 2d data when I...

``` using DiffEqOperators, Unitful nknots = 100 h = 1.0u"mm"/(nknots+1) Δ = CenteredDifference(2, 2, h, nknots) ``` results in an error

Appreciate your excellent works in SciML. I am struggling with a problem and really need help. Please !!! $$\mathcal{L} u = u_{xx} +u_{yy}, \quad \text{BCs:} \quad u(x+1,y)=u(x,y), u(x,y+1)= u(x,y).$$ I...

Congrats for the great work you are doing in the DiffEqOperators package. I was trying to create a 2D Laplacian matrix, but I can’t seem to manage to be able...

As per discussion earlier today with @ChrisRackauckas on slack, this PR extends `DiffEqOperators.calculate_weights` function to include recent algorithm of hermite-based finite difference weights by [fornberg(2020)](https://www.colorado.edu/amath/sites/default/files/attached-files/2020_f_hermite-fd_ima_j_num_anal.pdf) - The original fornberg(1988) algorithm...