Coef_func broken

[FuZhiyu]

I identified several issues with the coef_func:

Basic setup:

using DiffEqOperators
nknots = 10
h = 1.0/nknots
x = 1.0:10.0
bc = DirichletBC(0.0, 11.0)

Δ = CenteredDifference(1, 2, h, nknots)
Δ * (bc * x)

This returns a vector of 10, as expected.

If I pass any callable to the coef_func argument of CenteredDifference, the operator totally broke down:

Δ = CenteredDifference(1, 2, h, nknots, x-> h)
Δ * (bc * x)

This returns a vector of 0.

Of course, the coefficient for centereddifference function doesn't really matter, but other issues arise for UpwindDifference, mainly related with the treatment of boundaries:

Δ = UpwindDifference(1, 1, h, nknots, x-> h * x)
Δ * (bc * x)

This returns [1,2,1,2,3,4,5,6,-9,-10]. It seems that the coefficients are mismatched: They are only applied from the third entry. Also, there seem to be a problem with the right boundary.

If we concretize Δ, the mismatching is fixed:

Array(Δ) * (bc * x)

which returns [1,2,3,4,5,6,7,8,-9,-10], though there are still problems with the right boundary.

[ChrisRackauckas]

I am not sure anything with the upwind operators works, so I wouldn't be surprised if the coefficients are off there. For CenteredDifference it should be good though.

However, your function doesn't make sense. As the doc states:

An operational argument for a coefficient function f(du,u,p,t) which sets the coefficients of the operator.

I am actually surprised your example doesn't just error.

[FuZhiyu]

However, your function doesn't make sense. As the doc states:

An operational argument for a coefficient function f(du,u,p,t) which sets the coefficients of the operator.

I am actually surprised your example doesn't just error.

The documentation actually is very confusing to me, because in the current implementation, coef_func is a function that maps from the index of the x to the coefficient, as below quoted from derivative_operators.jl:

    for i in 1:len
        coefficients[i] = coeff_func(i)
    end