The finite-difference schemes of flux vector splitting for shallow water equations

The explicit and implicit finite-difference schemes based on the flux vector splitting (FVS) method for the numerical solution of the hyperbolic system of the fluid motion along the open channel was built.
The flux vector of original system in contrast to Euler equations in gas dynamics are not uniform functions. However the construction of schemes of FVS method using the theory of characteristics of hyperbolic equations is also possible in this case. The computing formulae are simple and handy. The possibilities of the schemes are illustrated by the test problems simulations.