Based on the algebra, revisit implementation and basis

[jlperla]

After #100 is done, revisit the formulas. In particular, never check types within a single function if at all possible, better map of code to algebra and use multiple-dispatch.

[jlperla]

When we do this, since everything will be written in terms of banded matrices, etc. we can use BandedMatrices.jl for both the unit tests and sometimes the implementation.

[chiyahn]

Use spdiag(-1 => foo, 2 => bar) instead (for now) as it's not clear how we can stack up the banded matrix L and the boundary condition matrix B together.