  The derivation of combined prefactored compact schemes for first and second
order derivatives is described here, relying on the Fourier analysis of the
original prefactored compact schemes. By this approach, the order of accuracy
of the original schemes can be increased from sixth to eight, or from eight to
tenth (depending on the order of the original scheme), while the number of grid
points in the stencil is kept the same. Here, we only frame the conceptual
derivation of the schemes, leading to a closed set of equations for the
weights.
