PROJECTIVE EIGENVALUE BOUNDS

In this second paper of a series, we revisit all major systematic uncertainties that affect a complete and unbiased sample of eleven finite difference schemes for advection-like equations. In order to provide the coherent picture, unlike the existing way, we use as the key tenets both the reverse Taylor’s analysis and the discrete Fourier’s analysis, as well as the monotonicity analysis. For every type of scheme, their theoretical uncertainties are examined. A detailed graphical investigation is also provided and used to give a physical reinterpretation of the Courant- Friedrichs-Lewy condition. We find that no scheme considered in this study resolves the smaller length scales well. Furthermore, we present several numerical experiments on an equal footing corroborating our demonstrations and proving to what degree the accuracy of each scheme is impaired by the discontinuities in the data. A comparison with each other is made as well. We definitively establish that the ingenious Lax- Wendroff scheme is preferred by experiments.