WENO methods

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]

  1. ^ 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.
  2. ^ 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.
  3. ^ 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.
  4. ^ 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.