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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 12
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Articles

Finite difference discretization of the Rosenau-RLW equation

Xintian Pan School of Mathematics and Information Science, Weifang University, Weifang, 261061, ChinaCorrespondence[email protected]
,
Kelong Zheng School of Science, Southwest University of Science and Technology, Mianyang, 621010, China
&
Luming Zhang Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
Pages 2578-2589 | Received 19 Jun 2012, Accepted 07 Nov 2012, Published online: 21 Dec 2012

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Mostafa Abbaszadeh & Mehdi Dehghan. (2018) The two-grid interpolating element free Galerkin (TG-IEFG) method for solving Rosenau-regularized long wave (RRLW) equation with error analysis. Applicable Analysis 97:7, pages 1129-1153.
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Articles from other publishers (26)

Sapna Pandit. (2024) A new algorithm for analysis and simulation of (2+1) Korteweg–de Vries–Rosenau-regularized long-wave model. Computational and Applied Mathematics 43:1.
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Akeel AL-saedi, Omid Nikan, Zakieh Avazzadeh & António Lopes. (2023) Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension. Symmetry 15:11, pages 1980.
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Wenju Zhao & Guang-Ri Piao. (2023) A reduced Galerkin finite element formulation based on proper orthogonal decomposition for the generalized KDV-RLW-Rosenau equation. Journal of Inequalities and Applications 2023:1.
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Mostafa Abbaszadeh, Mahmoud A. Zaky, Ahmed S. Hendy & Mehdi Dehghan. (2023) A two-grid spectral method to study of dynamics of dense discrete systems governed by Rosenau-Burgers' equation. Applied Numerical Mathematics 187, pages 262-276.
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Ankur, Ram Jiwari & Naresh Kumar. (2023) Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method. Computers & Mathematics with Applications 135, pages 134-148.
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Amit Kumar Verma & Mukesh Kumar Rawani. (2022) Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization . Numerical Methods for Partial Differential Equations 39:2, pages 1085-1107.
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Thanasak Mouktonglang, Suriyon Yimnet, Nattakorn Sukantamala & Ben Wongsaijai. (2022) Dynamical behaviors of the solution to a periodic initial–boundary value problem of the generalized Rosenau-RLW-Burgers equation. Mathematics and Computers in Simulation 196, pages 114-136.
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Sibel Özer & Nuri Murat Yağmurlu. (2022) Numerical solutions of nonhomogeneous Rosenau type equations by quintic B‐spline collocation method. Mathematical Methods in the Applied Sciences 45:9, pages 5545-5558.
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Ben Wongsaijai & Kanyuta Poochinapan. (2021) Optimal decay rates of the dissipative shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation with power of nonlinearity. Applied Mathematics and Computation 405, pages 126202.
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Selçuk Kutluay, Melike Karta & Yusuf Uçar. (2021) Strang time-splitting technique for the generalised Rosenau–RLW equation. Pramana 95:3.
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Yu.I. Dimitrienko, Shuguang Li & Yi Niu. (2021) Study on the dynamics of a nonlinear dispersion model in both 1D and 2D based on the fourth-order compact conservative difference scheme. Mathematics and Computers in Simulation 182, pages 661-689.
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N. Tamang, B. Wongsaijai, T. Mouktonglang & K. Poochinapan. (2020) Novel algorithm based on modification of Galerkin finite element method to general Rosenau-RLW equation in (2 + 1)-dimensions. Applied Numerical Mathematics 148, pages 109-130.
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Cui Guo, Fang Li, Wenping Zhang & Yuesheng Luo. (2019) A conservative numerical scheme for Rosenau-RLW equation based on multiple integral finite volume method. Boundary Value Problems 2019:1.
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Mostafa Abbaszadeh & Mehdi Dehghan. (2019) The interpolating element-free Galerkin method for solving Korteweg–de Vries–Rosenau-regularized long-wave equation with error analysis. Nonlinear Dynamics 96:2, pages 1345-1365.
Crossref
B. Wongsaijai, T. Mouktonglang, N. Sukantamala & K. Poochinapan. (2019) Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation. Applied Mathematics and Computation 340, pages 84-100.
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Xiaofeng Wang & Weizhong Dai. (2018) A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau–Kawahara-RLW equation. Computational and Applied Mathematics 37:5, pages 6560-6581.
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Alejandro Apolinar–Fernández & J.I. Ramos. (2018) Numerical solution of the generalized, dissipative KdV–RLW–Rosenau equation with a compact method. Communications in Nonlinear Science and Numerical Simulation 60, pages 165-183.
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Shuguang Li. (2016) Numerical analysis for fourth-order compact conservative difference scheme to solve the 3D Rosenau-RLW equation. Computers & Mathematics with Applications 72:9, pages 2388-2407.
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Bahar Korkmaz & Yilmaz Dereli. (2016) Numerical solution of the Rosenau- KdV -RLW equation by using RBFs collocation method . International Journal of Modern Physics C 27:10, pages 1650117.
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Dongdong He. (2016) Exact solitary solution and a three-level linearly implicit conservative finite difference method for the generalized Rosenau–Kawahara-RLW equation with generalized Novikov type perturbation. Nonlinear Dynamics 85:1, pages 479-498.
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J. I. Ramos & C. M. García-López. (2016) Solitary Wave Formation from a Generalized Rosenau Equation. Mathematical Problems in Engineering 2016, pages 1-17.
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Dongdong He & Kejia Pan. (2015) A linearly implicit conservative difference scheme for the generalized Rosenau–Kawahara-RLW equation. Applied Mathematics and Computation 271, pages 323-336.
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Dongdong He. (2015) New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity. Nonlinear Dynamics 82:3, pages 1177-1190.
Crossref
B. Wongsaijai & K. Poochinapan. (2014) A three-level average implicit finite difference scheme to solve equation obtained by coupling the Rosenau–KdV equation and the Rosenau–RLW equation. Applied Mathematics and Computation 245, pages 289-304.
Crossref
巍 高. (2014) A High Resolution NV/TVD Finite Volume Scheme for the Regularized Long Wave Equation. International Journal of Fluid Dynamics 02:01, pages 1-11.
Crossref
Tao Chen & Kaili Xiang. (2017) A New Nonlinear Conservative Difference Scheme for Generalized Rosenau-Kawahara Equation. SSRN Electronic Journal.
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