SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation (Journal of Mathematical Study, 2022)
In this article, we present a third-order weighted essentially non-oscillatory(WENO) method for generalized Rosenau-KdV-RLW equation. The third order finitedifference WENO reconstruction and central finite differences are applied to discreteadvection terms and other terms, respectively, in spatial discretization. In order toachieve the third order accuracy both in space and time, four stage third-order L-stableSSP Implicit-Explicit Runge-Kutta method (Third-order SSP EXRK method and third-order DIRK method) is applied to temporal discretization. The high order accuracyand essentially non-oscillatory property of finite difference WENO reconstruction areshown for solitary wave and shock wave for Rosenau-KdV and Rosenau-KdV-RLWequations. The efficiency, reliability and excellent SSP property of the numerical schemeare demonstrated by several numerical experiments with large CFL number.