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-Shan Jiang and Chi-Wang Shu developed a new WENO scheme2 called WENO-JS.3 Nowadays, there are many WENO methods.4
References
References
- Liu, Xu-Dong; Osher, Stanley; Chan, Tony (1994). "Weighted Essentially Non-oscillatory Schemes". Journal of Computational Physics. 115: 200–212. Bibcode:1994JCoPh.115..200L. CiteSeerX 10.1.1.24.8744. doi:10.1006/jcph.1994.1187.
- Jiang, Guang-Shan; Shu, Chi-Wang (1996). "Efficient Implementation of Weighted ENO Schemes". Journal of Computational Physics. 126 (1): 202–228. Bibcode:1996JCoPh.126..202J. CiteSeerX 10.1.1.7.6297. doi:10.1006/jcph.1996.0130.
- 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. arXiv:1106.3626. doi:10.1137/10080960X. S2CID 16602876.
Further reading
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. Vol. 1697. pp. 325–432. CiteSeerX 10.1.1.127.895. 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. Bibcode:2009SIAMR..51...82S. doi:10.1137/070679065.