A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation
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 treat...
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MDPI AG
2025-05-01
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| author | Yongzheng Li Longcheng Ren Jinsong Hu Kelong Zheng |
| author_facet | Yongzheng Li Longcheng Ren Jinsong Hu Kelong Zheng |
| author_sort | Yongzheng Li |
| collection | DOAJ |
| description | 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 <i>n</i>th and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></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. |
| format | Article |
| id | doaj-art-9079d3150b2f4113be776889f196b8bf |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-9079d3150b2f4113be776889f196b8bf2025-08-20T03:26:25ZengMDPI AGAxioms2075-16802025-05-0114639510.3390/axioms14060395A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW EquationYongzheng Li0Longcheng Ren1Jinsong Hu2Kelong Zheng3Faculty of Science, Civil Aviation Flight University of China, Guanghan 618307, ChinaFaculty of Science, Civil Aviation Flight University of China, Guanghan 618307, ChinaCollege of Big Data and Artificial Intelligence, Chengdu Technological University, Chengdu 6111730, ChinaFaculty of Science, Civil Aviation Flight University of China, Guanghan 618307, ChinaA 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 <i>n</i>th and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></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.https://www.mdpi.com/2075-1680/14/6/395Rosenau–RLW equationlinearized conservative difference schemesecond-order accuracyconvergencestability |
| spellingShingle | Yongzheng Li Longcheng Ren Jinsong Hu Kelong Zheng A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation Axioms Rosenau–RLW equation linearized conservative difference scheme second-order accuracy convergence stability |
| title | A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation |
| title_full | A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation |
| title_fullStr | A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation |
| title_full_unstemmed | A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation |
| title_short | A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation |
| title_sort | linearized conservative finite difference scheme for the rosenau rlw equation |
| topic | Rosenau–RLW equation linearized conservative difference scheme second-order accuracy convergence stability |
| url | https://www.mdpi.com/2075-1680/14/6/395 |
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