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SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation

SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation
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Year:    2022

Author:    Muyassar Ahmat, Jianxian Qiu

Journal of Mathematical Study, Vol. 55 (2022), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v55n1.22.01

Journal of Mathematical Study, Vol. 55 (2022), Iss. 1 : pp. 1–21

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

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

Author Details

Muyassar Ahmat

Jianxian Qiu

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