Simulations of shallow water equations by finite difference WENO schemes with multilevel time discretization

In this paper, we give a finite difference WENO schemes with multilevel time discretization for the computation of numerical solutions to one dimensional system hyperbolic conservation law. The method uses WENO schemes for spatial discretization and multilevel time discretization. Furthermore we give the application to the simulation of the one dimensional shallow water equations for the computational of physical observable, depth and velocity. Numerical examples are presented to validate the given this method.