TY - JOUR
T1 - SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation
AU - Ahmat , Muyassar
AU - Qiu , Jianxian
JO - Journal of Mathematical Study
VL - 1
SP - 1
EP - 21
PY - 2022
DA - 2022/01
SN - 55
DO - http://doi.org/10.4208/jms.v55n1.22.01
UR - https://global-sci.org/intro/article_detail/jms/20189.html
KW - Rosenau-KdV-RLW equation, WENO reconstruction, finite difference method, SSP implicit-explicit Runge-Kutta method.
AB - <p style="text-align: justify;">In this article, we present a third-order weighted essentially non-oscillatory
(WENO) method for generalized Rosenau-KdV-RLW equation. The third order finite
difference WENO reconstruction and central finite differences are applied to discrete
advection terms and other terms, respectively, in spatial discretization. In order to
achieve the third order accuracy both in space and time, four stage third-order L-stable
SSP Implicit-Explicit Runge-Kutta method (Third-order SSP EXRK method and third-order DIRK method) is applied to temporal discretization. The high order accuracy
and essentially non-oscillatory property of finite difference WENO reconstruction are
shown for solitary wave and shock wave for Rosenau-KdV and Rosenau-KdV-RLW
equations. The efficiency, reliability and excellent SSP property of the numerical scheme
are demonstrated by several numerical experiments with large CFL number.</p>