Family of symmetric bicompact schemes with spectral resolution property for hyperbolic equations

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 semidiscrete bicompact schemes of fourth to eighth orders of accuracy in space is performed. Numerical examples are presented that demonstrate the ability of the bicompact schemes to adequately simulate wave propagation, including short waves, on highly nonuniform grids at long times. The properties of solutions of the bicompact schemes in the problem of transfer of a stepwise initial profile are also considered.