A numerical study of SSP time integration methods for hyperbolic conservation laws

he method of lines approach for solving hyperbolic conservation laws is based on the idea of splitting the discretization process in two stages. First, the spatial discretization is performed by leaving the system continuous in time. This approximation is usually developed in a non-oscillatory manner with a satisfactory spatial accuracy. The obtained semi-discrete system of ordinary differential equations (ODE) is then solved by using some standard time integration method. In the last few years, a series of papers appeared, dealing with the high order strong stability preserving (SSP) time integration methods that maintain the total variation diminishing (TVD) property of the first order forward Euler method. In this work the optimal SSP Runge--Kutta methods of different order are considered in combination with the finite volume weighted essentially non-oscillatory (WENO) discretization. Furthermore, a new semi--implicit WENO scheme is presented and its properties in combination with different optimal implicit SSP Runge--Kutta methods are studied. Analysis is made on linear and nonlinear scalar equations and on Euler equations for gas dynamics