Volume 55, Issue 1
SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation

Muyassar Ahmat & Jianxian Qiu

J. Math. Study, 55 (2022), pp. 1-21.

Published online: 2022-01

Export citation
  • Abstract

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.

  • Keywords

Rosenau-KdV-RLW equation, WENO reconstruction, finite difference method, SSP implicit-explicit Runge-Kutta method.

  • AMS Subject Headings

65M60, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

muyassar@stu.xmu.edu.cn (Muyassar Ahmat)

jxqiu@xmu.edu.cn (Jianxian Qiu)

  • BibTex
  • RIS
  • TXT
@Article{JMS-55-1, author = {Muyassar and Ahmat and muyassar@stu.xmu.edu.cn and 22004 and School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen 361005, China and Muyassar Ahmat and Jianxian and Qiu and jxqiu@xmu.edu.cn and 11019 and School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen, Fujian 361005, P.R. China and Jianxian Qiu}, title = {SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {55}, number = {1}, pages = {1--21}, abstract = {

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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v55n1.22.01}, url = {http://global-sci.org/intro/article_detail/jms/20189.html} }
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 -

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.

Muyassar Ahmat & Jianxian Qiu. (2022). SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation. Journal of Mathematical Study. 55 (1). 1-21. doi:10.4208/jms.v55n1.22.01
Copy to clipboard
The citation has been copied to your clipboard