WENO methods explained
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
Further reading
- Book: 10.1007/BFb0096355 . Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws . Advanced Numerical Approximation of Nonlinear Hyperbolic Equations . 1697 . 325–432 . Lecture Notes in Mathematics . 1998 . Shu . Chi-Wang . 978-3-540-64977-9 . 10.1.1.127.895 .
- 10.1137/070679065 . High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems . SIAM Review . 51 . 82–126 . 2009 . Shu . Chi-Wang . 2009SIAMR..51...82S .
Notes and References
- 10.1006/jcph.1994.1187 . Weighted Essentially Non-oscillatory Schemes . Journal of Computational Physics . 115 . 200–212 . 1994 . Liu . Xu-Dong . Osher . Stanley . Chan . Tony . 1994JCoPh.115..200L . 10.1.1.24.8744 .
- 10.1006/jcph.1996.0130 . Efficient Implementation of Weighted ENO Schemes . Journal of Computational Physics . 126 . 202–228 . 1996 . Jiang . Guang-Shan . Shu . Chi-Wang . 1 . 1996JCoPh.126..202J . 10.1.1.7.6297 .
- 10.1016/j.jmaa.2012.04.040 . Mapped WENO schemes based on a new smoothness indicator for Hamilton–Jacobi equations . Journal of Mathematical Analysis and Applications . 394 . 2 . 670–682 . 2012 . Ha . Youngsoo . Kim . Chang Ho . Lee . Yeon Ju . Yoon . Jungho . free .
- 10.1137/10080960X . Strong Stability Preserving Two-step Runge–Kutta Methods . SIAM Journal on Numerical Analysis . 49 . 6 . 2618–2639 . 2011 . Ketcheson . David I. . Gottlieb . Sigal . MacDonald . Colin B. . 1106.3626 . 16602876 .
