A fourth‐order central Runge‐Kutta scheme for hyperbolic conservation laws

Abstract

Abstract In this work, a new formulation for a central scheme recently introduced by A. A. I. Peer et al. is performed. It is based on the staggered grids. For this work, first a time discritization is carried out, followed by the space discritization. Spatial accuracy is obtained using a piecewise cubic polynomial and fourth‐order numerical derivatives. Time accuracy is obtained applying a Runge‐Kutta(RK) scheme. The scheme proposed in this work has a simpler structure than the central scheme developed in (Peer et al., Appl Numer Math 58 (2008), 674–688). Several standard one‐dimensional test cases are used to verify high‐order accuracy, nonoscillatory behavior, and good resolution properties for smooth and discontinuous solutions. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010