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Applicable Analysis
An International Journal
Volume 77, 2001 - Issue 3-4
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Original Articles

Numerical methods for the rosenau equation

Rosenau equation

Sank K. Chunk Department of Mathematics Education, Seoul National University, Seoul, 151–742, Korea
&
Amiya K. Pani Department of Mathematics Education, Seoul National University, Seoul, 151–742, Korea
Pages 351-369 | Received 01 Jul 2000, Published online: 02 May 2007

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Mohammad Tanzil Hasan & Chuanju Xu. (2020) The stability and convergence of time-stepping/spectral methods with asymptotic behaviour for the Rosenau–Burgers equation. Applicable Analysis 99:12, pages 2013-2025.
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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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Ahlem Ghiloufi & Tlili Kadri. (2017) Analysis of new conservative difference scheme for two-dimensional Rosenau-RLW equation. Applicable Analysis 96:7, pages 1255-1267.
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Noureddine Atouani & Khaled Omrani. (2015) A new conservative high-order accurate difference scheme for the Rosenau equation. Applicable Analysis 94:12, pages 2435-2455.
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Xintian Pan, Kelong Zheng & Luming Zhang. (2013) Finite difference discretization of the Rosenau-RLW equation. Applicable Analysis 92:12, pages 2578-2589.
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Articles from other publishers (56)

Wanying Mao, Qifeng Zhang, Dinghua Xu & Yinghong Xu. (2024) Double reduction order method based conservative compact schemes for the Rosenau equation. Applied Numerical Mathematics 197, pages 15-45.
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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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Xintian Pan & Luming Zhang. (2023) A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation. Demonstratio Mathematica 56:1.
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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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Ömer Oruç. (2023) Integrated Chebyshev wavelets for numerical solution of nonlinear one-dimensional and two-dimensional Rosenau equations. Wave Motion 118, pages 103107.
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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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L. Jones Tarcius Doss & L. Aishwarya. (2023) An $$H^{1}-$$Galerkin mixed finite element method for rosenau equation. Computational and Applied Mathematics 42:3.
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Dongyang Shi & Xu Jia. (2023) Convergence analysis of the Galerkin finite element method for the fourth-order Rosenau equation. Applied Mathematics Letters 135, pages 108432.
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P. Danumjaya & K. Balaje. (2022) Discontinuous Galerkin finite element methods for one-dimensional Rosenau equation. The Journal of Analysis 30:4, pages 1407-1426.
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Giuseppe Maria Coclite & Lorenzo di Ruvo. (2022) On the classical solutions for a Rosenau–Korteweg-deVries–Kawahara type equation. Asymptotic Analysis 129:1, pages 51-73.
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Asma Rouatbi, Ahlem Ghiloufi & Khaled Omrani. (2022) An efficient tool for solving the Rosenau–Burgers equation in two dimensions. Computational and Applied Mathematics 41:5.
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Kamal Rashedi. (2022) A spectral method based on Bernstein orthonormal basis functions for solving an inverse Roseneau equation. Computational and Applied Mathematics 41:5.
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Sanjay Kumar, Ram Jiwari & R.C. Mittal. (2022) Radial basis functions based meshfree schemes for the simulation of non-linear extended Fisher–Kolmogorov model. Wave Motion 109, pages 102863.
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Ali Demirci, Yasin Hasanoğlu, Gulcin M. Muslu & Cihangir Özemir. (2022) On the Rosenau equation: Lie symmetries, periodic solutions and solitary wave dynamics. Wave Motion 109, pages 102848.
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Khaled Omrani, Hajer Debebria & Khedidja Bayarassou. (2020) On the numerical solution of two-dimensional Rosenau–Burgers (RB) equation. Engineering with Computers 38:1, pages 715-726.
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Khaled Omrani & Ahlem Ghiloufi. (2020) An efficient computational approach for two-dimensional variant of nonlinear-dispersive model of shallow water wave. Engineering with Computers 37:4, pages 2679-2688.
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Dongyang Shi & Xu Jia. (2021) Nonconforming Quasi-Wilson finite element approximation for the nonlinear Rosenau equation. Applied Mathematics Letters 119, pages 107238.
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Yanjie Zhou, Yanan Zhang, Ye Liang & Zhendong Luo. (2021) A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation. Applied Numerical Mathematics 162, pages 192-200.
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Maosheng Jiang, Luiz Bevilacqua, Jiang Zhu & Xijun Yu. (2020) Nonlinear Galerkin finite element methods for fourth-order Bi-flux diffusion model with nonlinear reaction term. Computational and Applied Mathematics 39:3.
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Mostafa Abbaszadeh, Mehdi Dehghan, Amirreza Khodadadian & Clemens Heitzinger. (2020) Error analysis of interpolating element free Galerkin method to solve non-linear extended Fisher–Kolmogorov equation. Computers & Mathematics with Applications 80:1, pages 247-262.
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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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Dongyang Shi & Xu Jia. (2020) Superconvergence analysis of the mixed finite element method for the Rosenau equation. Journal of Mathematical Analysis and Applications 481:1, pages 123485.
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Zhang Jun. (2019) Numerical Methods for a Shallow Water Rosenau-Burgers Equation. IOP Conference Series: Earth and Environmental Science 252, pages 052123.
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Fatma Zürnacı & Muaz Seydaoğlu. (2019) On the convergence of operator splitting for the Rosenau–Burgers equation. Numerical Methods for Partial Differential Equations 35:4, pages 1363-1382.
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Jun Zhang, Zixin Liu, Fubiao Lin & Jianjun Jiao. (2019) Asymptotic Analysis and Error Estimate for Rosenau-Burgers Equation. Mathematical Problems in Engineering 2019, pages 1-8.
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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.
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L. Jones Tarcius Doss & A. P. Nandini. (2018) A fourth‐order H 1 ‐Galerkin mixed finite element method for Kuramoto–Sivashinsky equation . Numerical Methods for Partial Differential Equations 35:2, pages 445-477.
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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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Noureddine Atouani, Yousra Ouali & Khaled Omrani. (2017) Mixed finite element methods for the Rosenau equation. Journal of Applied Mathematics and Computing 57:1-2, pages 393-420.
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Ali Safdari-Vaighani, Elisabeth Larsson & Alfa Heryudono. (2017) Radial Basis Function Methods for the Rosenau Equation and Other Higher Order PDEs. Journal of Scientific Computing 75:3, pages 1555-1580.
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Ahlem Ghiloufi & Khaled Omrani. (2017) New conservative difference schemes with fourth‐order accuracy for some model equation for nonlinear dispersive waves. Numerical Methods for Partial Differential Equations 34:2, pages 451-500.
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Asma Rouatbi, Moeiz Rouis & Khaled Omrani. (2017) Numerical scheme for a model of shallow water waves in -dimensions . Computers & Mathematics with Applications 74:8, pages 1871-1884.
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Giuseppe Maria Coclite & Lorenzo di Ruvo. (2017) On the convergence of the modified Rosenau and the modified Benjamin–Bona–Mahony equations. Computers & Mathematics with Applications 74:5, pages 899-919.
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Giuseppe Maria Coclite & Lorenzo di Ruvo. (2017) A singular limit problem for conservation laws related to the Rosenau–Korteweg–de Vries equation. Journal de Mathématiques Pures et Appliquées 107:3, pages 315-335.
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Guang-Ri Piao, June-Yub Lee & Guo-Xian Cai. (2016) Analysis and computational method based on quadratic B-spline FEM for the Rosenau-Burgers equation. Numerical Methods for Partial Differential Equations 32:3, pages 877-895.
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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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Xintian Pan, Yiju Wang & Luming Zhang. (2015) Numerical analysis of a pseudo-compact C-N conservative scheme for the Rosenau-KdV equation coupling with the Rosenau-RLW equation. Boundary Value Problems 2015:1.
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Shubin Wang & Xiao Su. (2015) Global existence and asymptotic behavior of solution for Rosenau equation with Stokes damped term. Mathematical Methods in the Applied Sciences 38:17, pages 3990-4000.
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S.G. Pyatkov & S.N. Shergin. (2015) On Some Mathematical Models of Filtration Theory. Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 8:2, pages 105-116.
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Noureddine Atouani & Khaled Omrani. (2015) On the convergence of conservative difference schemes for the 2D generalized Rosenau–Korteweg de Vries equation. Applied Mathematics and Computation 250, pages 832-847.
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Jinsong Hu, Youcai Xu, Bing Hu & Xiaoping Xie. (2014) Two Conservative Difference Schemes for Rosenau-Kawahara Equation. Advances in Mathematical Physics 2014, pages 1-11.
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Maobo Zheng & Jun Zhou. (2014) An Average Linear Difference Scheme for the Generalized Rosenau-KdV Equation. Journal of Applied Mathematics 2014, pages 1-9.
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Guan-Yu Xue & Luming Zhang. (2013) A new finite difference scheme for generalized Rosenau–Burgers equation. Applied Mathematics and Computation 222, pages 490-496.
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Noureddine Atouani & Khaled Omrani. (2013) Galerkin finite element method for the Rosenau-RLW equation. Computers & Mathematics with Applications 66:3, pages 289-303.
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Jinsong Hu & Yulan Wang. (2013) A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation. Mathematical Problems in Engineering 2013, pages 1-8.
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Jinsong Hu, Youcai Xu & Bing Hu. (2013) Conservative Linear Difference Scheme for Rosenau-KdV Equation. Advances in Mathematical Physics 2013, pages 1-7.
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Xintian Pan & Luming Zhang. (2012) A new finite difference scheme for the Rosenau–Burgers equation. Applied Mathematics and Computation 218:17, pages 8917-8924.
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Jinsong Hu, Bing Hu & Youcai Xu. (2011) Average implicit linear difference scheme for generalized Rosenau–Burgers equation. Applied Mathematics and Computation 217:19, pages 7557-7563.
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Jinsong Hu & Kelong Zheng. (2010) Two Conservative Difference Schemes for the Generalized Rosenau Equation. Boundary Value Problems 2010:1, pages 543503.
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Desheng Li, Zhuangzhuang Wang, Yongbing Wu & Yao Lu. (2009) A Finite Difference Simulation for Rosenau-Burgers Equation. A Finite Difference Simulation for Rosenau-Burgers Equation.
Bing Hu, Youcai Xu & Jinsong Hu. (2008) Crank–Nicolson finite difference scheme for the Rosenau–Burgers equation. Applied Mathematics and Computation 204:1, pages 311-316.
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Khaled Omrani, Faycal Abidi, Talha Achouri & Noomen Khiari. (2008) A new conservative finite difference scheme for the Rosenau equation. Applied Mathematics and Computation 201:1-2, pages 35-43.
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S.M. Choo, S.K. Chung & K.I. Kim. (2008) A discontinuous Galerkin method for the Rosenau equation. Applied Numerical Mathematics 58:6, pages 783-799.
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M. O. Korpusov & A. G. Sveshnikov. (2008) Blow-up of solutions of strongly nonlinear equations of pseudoparabolic type. Journal of Mathematical Sciences 148:1, pages 1-142.
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M. O. Korpusov & A. G. Sveshnikov. (2005) On the “Destruction” of Solutions of Nonlinear Wave Equations of Sobolev Type with Cubic Sources. Mathematical Notes 78:3-4, pages 518-536.
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Максим Олегович Корпусов, Maxim Olegovich Korpusov, Алексей Георгиевич Свешников & Aleksei Georgievich Sveshnikov. (2005) О “разрушении” решений нелинейных волновых уравнений типа Соболева с кубическими источникамиOn the “Destruction” of Solutions of Nonlinear Wave Equations of Sobolev Type with Cubic Sources. Математические заметки Matematicheskie Zametki 78:4, pages 559-578.
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