A sixth-order bicompact scheme with spectral-like resolution for hyperbolic equations

Abstract

For the numerical solution of nonstationary quasilinear hyperbolic equations, a family of symmetric semidiscrete bicompact schemes based on collocation polynomials is constructed in the one- and multidimensional cases. A dispersion analysis of a semidiscrete bicompact scheme of six-order accuracy in space is performed. It is proved that the dispersion properties of the scheme are preserved on highly nonuniform spatial grids. It is shown that the phase error of the sixth-order bicompact scheme does not exceed 0.2% in the entire range of dimensionless wave numbers. A numerical example is presented that demonstrates the ability of the bicompact scheme to adequately simulate wave propagation on coarse grids at long times.