Quasimonotone difference schemes for some systems of first order hyperbolic equations

The quasimonotone finite-difference schemes based on the flux vector splitting method for the numerical solution of nonviscous nonheat gas flows and also the fluid motion along the open channel was built. Some modified notations for split flux of Van Leer are used. A new type of function-analyser of smoothing, which improve computing properties of schemes, is suggested.
The possibilities of the schemes are illustrated by the test problems simulations.