Arbitrary high-order linearly implicit energy-conserving schemes for the Rosenau-type equation. (April 2023)

• Record Type: Journal Article
• Authors: Zhang, Wei; Liu, Chunxia; Jiang, Chaolong; Zheng, Chenxuan
• Is Part Of: Applied mathematics letters. Volume 138(2023)
• Publication Date: 2023-04
• Subjects: Energy-conserving -- High-order -- Linearly implicit scheme -- Rosenau equation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108530
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we present a class of high-order linearly implicit energy-conserving schemes for solving the generalized Rosenau-type equation. We firstly reformulate the equation into a skew-adjoint system with the energy conservation law. Then the nonlinear terms of the system are approximated with an extrapolation/prediction–correction technique and then a linearized energy-conserving system is obtained. Finally, the symplectic Runge–Kutta method in time and the Fourier pseudo-spectral method in space are employed to discretize the resulting linearized system and a fully discrete scheme is obtained, which is linearly implicit, high-order and energy-conserving. Numerical results are addressed to demonstrate the accuracy and efficiency of the proposed scheme.