The problem of the construction of optimal finite-difference schemes for linear advection equations is considered. These equations are solved on the stage of the splitting method for the solution of kinetic equations. Construction of optimal schemes is based on the solution of the problem of minimization of dispersive and dissipative characteristics of finite-difference scheme. These characteristics are constructed as maximum functions. Constructed optimal schemes may be used in lattice Boltzmann method for modelling of fluid and gas flows.