(a) Harmonic analysis of the dispersion relation c′/c and (b) the error |k′Δx − kΔx|_real of different finite-difference-stencils for first order partial differential equations. (c) CPU-time with respect to the error. For the analysis, the vector length was chosen to match PPW resolution and dispersion error from (b). The short forms OX denote the order, exp or imp, explicit or implicit / compact derivatives (Eq. (8)). The error of 10⁻³ is highlighted by a black dotted line as it is used for discussion the text.