A fourth-order central Runge-Kutta scheme for hyperbolic conservation laws.

*(English)*Zbl 1200.65074Summary: A new formulation for a central scheme recently introduced by A. A. I. Peer et al. [Appl. Numer. Math. 58, No. 5, 674–688 (2008; Zbl 1138.65075)] is presented. It is based on staggered grids. For this work, first a time discretization is carried out, followed by a space discretization. Spatial accuracy is obtained using piecewise cubic polynomial and fourth-order numerical derivatives. Time accuracy is obtained applying a Runge-Kutta scheme. The scheme proposed in this work has a simpler structure than the central scheme developed in [loc. cit.]. Several standard one-dimensional test cases are used to verify high-order accuracy, nonoscillatory behavior, and good resolution properties for smooth and discontinuous solutions.

##### MSC:

65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |

##### Keywords:

central Runge-Kutta (CRK) scheme; central scheme; hyperbolic conservation laws; nonlinear limiters; nonoscillatory scheme; weighted essentially nonoscillatory (WENO) technique
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\textit{M. Dehghan} and \textit{R. Jazlanian}, Numer. Methods Partial Differ. Equations 26, No. 6, 1675--1692 (2010; Zbl 1200.65074)

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