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A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation

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Publicado en:Axioms vol. 14, no. 6 (2025), p. 395
Autor principal: Li Yongzheng
Otros Autores: Ren Longcheng, Hu, Jinsong, Zheng Kelong
Publicado:
MDPI AG
Materias:
Propagation
Finite volume method
Numerical analysis
Linearization
Accuracy
Mathematical analysis
Energy methods
Boundary value problems
Finite difference method
Discretization
Crank-Nicholson method
Acceso en línea:Citation/Abstract
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Resumen:A novel two–level linearized conservative finite difference method is proposed for solving the initial boundary value problem of the Rosenau–RLW equation. To preserve the energy conservation property, the Crank–Nicolson scheme is employed for temporal discretization, combined with an averaging treatment of the nonlinear term between the nth and <inline-formula>(n+1)</inline-formula>th time levels. For spatial discretization, a centered symmetric scheme is adopted. Meanwhile, the discrete conservation law is presented, and the existence and uniqueness of the numerical solutions are rigorously proved. Furthermore, the convergence and stability of the scheme are analyzed using the discrete energy method. Numerical experiments validate the theoretical results.
ISSN:2075-1680
DOI:10.3390/axioms14060395
Fuente:Engineering Database