(Peer-Reviewed) SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation
Muyassar Ahmat, Jianxian Qiu 邱建贤
School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen 361005, China
中国 厦门 厦门大学数学科学学院 福建省数学建模与高性能科学计算重点实验室
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 thirdorder 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.
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