  A generalized prefactorization of compact schemes aimed at reducing the
stencil and improving the computational efficiency is proposed here in the
framework of transport equations. By the prefactorization introduced here, the
computational load associated with inverting multi-diagonal matrices is
avoided, while the order of accuracy is preserved. The prefactorization can be
applied to any centered compact difference scheme with arbitrary order of
accuracy (results for compact schemes of up to sixteenth order of accuracy are
included in the study). One notable restriction is that the proposed schemes
can be applied in a predictor-corrector type marching scheme framework. Two
test cases, associated with linear and nonlinear advection equations,
respectively, are included to show the preservation of the order of accuracy
and the increase of the computational efficiency of the prefactored compact
schemes.
