On a large time-step high resolution scheme

This paper presents a class of new second-order accurate ( 2 K + 3 ) (2K + 3) -point explicit schemes for the computation of weak solutions of hyperbolic conservation laws, that are total-variation-diminishing under a CFL restriction of K . These highly nonlinear schemes are obtained by applying a nonoscillatory first-order accurate ( 2 K + 1 ) (2K + 1) -point scheme to a modified flux. The so-derived second-order accurate schemes achieve high resolution, while retaining the robustness of the original first-order accurate scheme.