基于双约阶法的Rosenau-Burgers方程的线性化保守紧格式

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-04 DOI:10.1016/j.cnsns.2025.108974

Sitong Dong, Yiran Zhang, Yuanfeng Jin

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引用次数: 0

摘要

在空间周期边界条件下，基于二阶约简法和四阶紧算子，提出了求解Rosenau-Burgers方程的三阶线性化差分格式。讨论了该差分格式的守恒律、可解性和收敛性。该方案具有二阶时间收敛性和四阶空间收敛性。数值模拟结果与理论分析吻合较好。

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A linearized conservative compact scheme based on the double reduction order method for the Rosenau–Burgers equation

In this paper, we propose a three-level linearized difference scheme to solve the Rosenau–Burgers equation based on the double reduction order method and the fourth-order compact operator under the spatial periodic boundary conditions. We discuss the conservation law, solvability, and convergence for this difference scheme. The proposed scheme has second-order temporal and fourth-order spatial convergence. Numerical simulations are also provided which agree well with our theoretical analysis.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.