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Li S, Fu H. A new high-order compact and conservative numerical scheme for the generalized symmetric regularized long wave equations. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2023; 100:968-990. [DOI: 10.1080/00207160.2023.2167516] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Revised: 01/07/2023] [Accepted: 01/08/2023] [Indexed: 01/04/2025]
Affiliation(s)
- Shuguang Li
- School of Science, Dalian Maritime University, Dalian, China
| | - Hongsun Fu
- School of Science, Dalian Maritime University, Dalian, China
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Fu Z, Guo Z, Hu JS, Zhang ZY. A decoupled high accuracy linear difference scheme for symmetric regularized long wave equation with damping term. THERMAL SCIENCE 2022; 26:1061-1068. [DOI: 10.2298/tsci2202061f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2025]
Abstract
In this paper, the initial boundary value problem of the dissipative
symmetric regularized long wave equation with a damping term is studied
numerically, and a decoupled linearized difference scheme with a theoretical
accuracy of O(?2+h4)is proposed. Because the scheme removes the coupling between the
variables in the original equation, the linearized difference scheme and the
ex-plicit difference scheme can be used to solve the two variables in
parallel, which greatly improves the efficiency of numerical solutions. To
obtain the maximum norm estimation of numerical solutions, the mathematical
induction and the discrete functional analysis methods are introduced
directly to prove the convergence and the stability of the scheme.
Numerical experiments have also verified the reliability of the proposed
scheme.
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Affiliation(s)
- Zhen Fu
- School of Science, Xihua University, Chengdu, China
| | - Zhen Guo
- School of Science, Xihua University, Chengdu, China
| | - Jin-Song Hu
- School of Science, Xihua University, Chengdu, China
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Mittal RC, Tripathi A. Numerical Solutions of Symmetric Regularized Long Wave Equations Using Collocation of Cubic B-splines Finite Element. INTERNATIONAL JOURNAL FOR COMPUTATIONAL METHODS IN ENGINEERING SCIENCE AND MECHANICS 2015; 16:142-150. [DOI: 10.1080/15502287.2015.1011812] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2025]
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Zhao M, Liu Y, Li H. Fully discrete two-step mixed element method for the symmetric regularized long wave equation. INTERNATIONAL JOURNAL OF MODELING, SIMULATION, AND SCIENTIFIC COMPUTING 2014; 05:1450007. [DOI: 10.1142/s179396231450007x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2025]
Abstract
A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave (SRLW) equation. The optimal a priori error estimates (O((Δt)2 + hm+1 + hk+1)) for fully discrete explicit two-step mixed scheme are derived. Moreover, a numerical example is provided to confirm our theoretical results.
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Affiliation(s)
- Meng Zhao
- School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China
| | - Yang Liu
- School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China
| | - Hong Li
- School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China
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Xu Y, Hu B, Xie X, Hu J. Mixed finite element analysis for dissipative SRLW equations with damping term. APPLIED MATHEMATICS AND COMPUTATION 2012; 218:4788-4797. [DOI: 10.1016/j.amc.2011.10.020] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
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