Essentially non-oscillatory (ENO) and Weighted ENO (WENO) are finite difference or finite volume schemes. The first ENO scheme is constructed by Harten et. al. in 1987. The first WENO scheme is constructed in 1994 by Liu,Osher and Chan for a third order finite volume version. In 1996, third and fifth order finite difference WENO schemes in multi space dimensions are constructed by Jiang and Shu, with a general framework for the design of smoothness indicators and nonlinear weights. A key idea in WENO schemes is a linear combination of lower order fluxes or reconstruction to obtain a higher order approximation. Both ENO and WENO schemes use the idea of adaptive stencils to automatically achieve high order accuracy and non-oscillatory property near discontinuities. or the system case, WENO schemes based on local characteristic decompositions and flux splitting to avoid spurious oscillatory.

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