WENO methods
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Short description: Scheme used in the numerical solution of hyperbolic partial differential equations
In numerical solution of differential equations, WENO (weighted essentially non-oscillatory) methods are classes of high-resolution schemes. WENO are used in the numerical solution of hyperbolic partial differential equations. These methods were developed from ENO methods (essentially non-oscillatory). The first WENO scheme was developed by Liu, Osher and Chan in 1994.[1] In 1996, Guang-Sh and Chi-Wang Shu developed a new WENO scheme[2] called WENO-JS.[3] Nowadays, there are many WENO methods.[4]
See also
References
- ↑ Liu, Xu-Dong; Osher, Stanley; Chan, Tony (1994). "Weighted Essentially Non-oscillatory Schemes". Journal of Computational Physics 115: 200–212. doi:10.1006/jcph.1994.1187. Bibcode: 1994JCoPh.115..200L.
- ↑ Jiang, Guang-Shan; Shu, Chi-Wang (1996). "Efficient Implementation of Weighted ENO Schemes". Journal of Computational Physics 126 (1): 202–228. doi:10.1006/jcph.1996.0130. Bibcode: 1996JCoPh.126..202J.
- ↑ Ha, Youngsoo; Kim, Chang Ho; Lee, Yeon Ju; Yoon, Jungho (2012). "Mapped WENO schemes based on a new smoothness indicator for Hamilton–Jacobi equations". Journal of Mathematical Analysis and Applications 394 (2): 670–682. doi:10.1016/j.jmaa.2012.04.040.
- ↑ Ketcheson, David I.; Gottlieb, Sigal; MacDonald, Colin B. (2011). "Strong Stability Preserving Two-step Runge–Kutta Methods". SIAM Journal on Numerical Analysis 49 (6): 2618–2639. doi:10.1137/10080960X.
Further reading
- Shu, Chi-Wang (1998). "Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws". Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Lecture Notes in Mathematics. 1697. pp. 325–432. doi:10.1007/BFb0096355. ISBN 978-3-540-64977-9.
- Shu, Chi-Wang (2009). "High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems". SIAM Review 51: 82–126. doi:10.1137/070679065. Bibcode: 2009SIAMR..51...82S.
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