High order central schemes for hyperbolic systems of conservation laws

In this talk we present third and fourth order central schemes for the approximate solution of quasilinear systems of conservation laws. The schemes are an extension of the second order Nessyahu-Tadmor scheme, and are based on a ENO reconstruction from cell averages, and a numerical computation of the flux on cell boundaries, efficiently obtained by Runge-Kutta schemes with Natural Continuous Extension. Here we focus on the linear stability analysis of the scheme. The exact CFL condition for linear third and fourth order schemes are derived.