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We present a family of high-order, essentially non-oscillatory, central schemes for approx- imating solutions of hyperbolic systems of conservation laws. These schemes are based on a new centered version of the Weighed Essentially Non-Oscillatory (WENO) reconstruction of point-values from cell-averages, which is then followed by an accurate approximation of the fluxes via a natural con- tinuous extension of Runge-Kutta solvers. We explicitly construct the third and fourth-order scheme and demonstrate their high-resolution properties in several numerical tests. R esum e. Nous pr esentons une famille de sch emas centr es ENO d'ordre elev e pour des solutions approch ees de syst emes hyperboliques de lois de conservation. Ces sch emas reposent sur une nouvelle version centr ee de la reconstruction ENO a poids (WENO) des valeurs ponctuelles a partir des moyennes sur les cellules, ce qui conduit a une approximation precise des flux gr^ ace a une extension naturelle continue des solveurs Runge-Kutta. Nous construisons explicitement les sch emas d'ordre trois et quatre et nous provons leurs propri et es de haute pr ecision a travers des essais num eriques.

Central WENO schemes for hyperbolic systems of conservation laws