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The derivation of combined prefactored compact schemes for first and secondorder derivatives is described here, relying on the Fourier analysis of theoriginal prefactored compact schemes. By this approach, the order of accuracyof the original schemes can be increased from sixth to eight, or from eight totenth (depending on the order of the original scheme), while the number of gridpoints in the stencil is kept the same. Here, we only frame the conceptualderivation of the schemes, leading to a closed set of equations for theweights.

Combined prefactored compact schemes for first- and second-order derivatives: conceptual derivation