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Applicable Analysis
An International Journal
Volume 54, 1994 - Issue 1-2
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Original Articles

Finite element galerkin solutions for the rosenau equation

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Pages 39-56 | Received 10 Apr 1993, Published online: 02 May 2007

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Read on this site (8)

Supreedee Dangskul & Teeranush Suebcharoen. (2022) Evaluation of shallow water waves modelled by the Rosenau-Kawahara equation using pseudo-compact finite difference approach. International Journal of Computer Mathematics 99:8, pages 1617-1637.
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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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Sank K. Chunk & Amiya K. Pani. (2001) Numerical methods for the rosenau equation. Applicable Analysis 77:3-4, pages 351-369.
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S.K. CHUNG. (1998) Finite Difference Approximate Solutions for. Applicable Analysis 69:1-2, pages 149-156.
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Mei Ming. (1998) Long-time behaviour of solution for rosenau-burgers equation(II). Applicable Analysis 68:3-4, pages 333-356.
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Mei Ming. (1996) Long-time behavior of solution for rosenau-burgers equation (i). Applicable Analysis 63:3-4, pages 315-330.
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Articles from other publishers (53)

Ankur & Ram Jiwari. (2024) A new error estimates of finite element method for (2+1)-dimensional nonlinear advection-diffusion model. Applied Numerical Mathematics 198, pages 22-42.
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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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Ankur & Ram Jiwari. (2023) New multiple analytic solitonary solutions and simulation of (2+1)-dimensional generalized Benjamin-Bona-Mahony-Burgers model. Nonlinear Dynamics 111:14, pages 13297-13325.
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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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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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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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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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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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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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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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Ben Wongsaijai, Phakdi Charoensawan, Tanadon Chaobankoh & Kanyuta Poochinapan. (2021) Advance in compact structure‐preserving manner to the Rosenau–Kawahara model of shallow‐water wave. Mathematical Methods in the Applied Sciences 44:8, pages 7048-7064.
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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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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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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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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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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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Akram Saeedi & Reza Pourgholi. (2017) Application of quintic B-splines collocation method for solving inverse Rosenau equation with Dirichlet’s boundary conditions. Engineering with Computers 33:3, pages 335-348.
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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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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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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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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.
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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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Hongwei Wang & Shubin Wang. (2013) Global existence and asymptotic behavior of solution for the Rosenau equation with hydrodynamical damped term. Journal of Mathematical Analysis and Applications 401:2, pages 763-773.
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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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Hongwei Wang & Shubin Wang. (2011) Decay and scattering of small solutions for Rosenau equations. Applied Mathematics and Computation 218:1, pages 115-123.
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Amin Esfahani. (2011) Solitary Wave Solutions for Generalized Rosenau-KdV Equation. Communications in Theoretical Physics 55:3, pages 396-398.
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Shubin Wang & Guixiang Xu. (2009) The Cauchy problem for the Rosenau equation. Nonlinear Analysis: Theory, Methods & Applications 71:1-2, pages 456-466.
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Tlili Kadri, Noomen Khiari, Faycal Abidi & Khaled Omrani. (2008) Methods for the numerical solution of the Benjamin‐Bona‐Mahony‐Burgers equation. Numerical Methods for Partial Differential Equations 24:6, pages 1501-1516.
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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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Liping Liu, Ming Mei & Yau Shu Wong. (2007) Asymptotic behavior of solutions to the Rosenau–Burgers equation with a periodic initial boundary. Nonlinear Analysis: Theory, Methods & Applications 67:8, pages 2527-2539.
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Liping Liu & Ming Mei. (2002) A better asymptotic profile of Rosenau–Burgers equation. Applied Mathematics and Computation 131:1, pages 147-170.
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