On spectral-like resolution properties of fourth-order accurate symmetric bicompact schemes

Abstract

A dispersion analysis is conducted for bicompact schemes of fourth-order accuracy in space, namely, for a semidiscrete scheme and a second-order accurate scheme in time. It is shown that their numerical group velocity is positive for all dimensionless wavenumbers. It is proved that the dispersion properties of the bicompact schemes are preserved on highly nonuniform meshes. A comparison reveals that the fourth-order bicompact schemes have a higher spectral resolution than not only other same-order compact schemes, but also some sixth-order ones. Two numerical examples are presented that demonstrate the ability of the bicompact schemes to adequately simulate wave propagation on highly nonuniform meshes over long time intervals.