I think an example of how this BC handling works for spectral operators would be a good thing to add to the writeup. Essentially, you can write out Dirichlet and Neumann conditions as summation conditions in the function space (just plug in x and evaluate). The summation condition is just a row/column of the operator. This defines how you would have to extrapolate to a larger function space that satisfies the conditions, and then the differentiation operator brings it back down.
I think an example of how this BC handling works for spectral operators would be a good thing to add to the writeup. Essentially, you can write out Dirichlet and Neumann conditions as summation conditions in the function space (just plug in
xand evaluate). The summation condition is just a row/column of the operator. This defines how you would have to extrapolate to a larger function space that satisfies the conditions, and then the differentiation operator brings it back down.