Feature request: Derivative boundary condition for BVP ODEs

[yewalenikhil65]

At the moment BoundaryValueDiffEq doesn't seem to support derivative boundary conditions(neumann, robin) at the boundaries in ODEs of BVP form. Requesting maintainers for same !

[cpf-work]

I'm not 100% sure whether I'm correct here, and it is probably not efficient. But I think you can take your differential equation function to calculate the derivatives at the boundaries and use those to calculate the residual in the BCs.

[ChrisRackauckas]

The interpolation function that is used for computing u(t) in the multi-point boundary conditions can just be analytically differentiated. We just need to support the same syntax as the ODE solver, i.e. u(t, Val{1}) for the first derivative, and then this can be treated as a multipoint BVP.