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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 12
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Articles

Numerical analysis of a new conservative scheme for the 2D generalized Rosenau-RLW equation

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Pages 2564-2580 | Received 30 Jun 2019, Accepted 07 Nov 2019, Published online: 17 Nov 2019

References

  • Amorim P, Figueira M. Convergenceof a finite difference method for the KdV and modified KdV equations with L2 data. Port Math. 2013;70(1):23–50. doi: 10.4171/PM/1924
  • Zhang X, Zhang P. A reduced high-order compact finite difference scheme based on proper orthogonal decomposition technique for KdV equation. Appl Math Comput. 2018;339:535–545. doi: 10.1016/j.cam.2017.09.045
  • Siraj-ul-Islam, Haq S, Ali A. A meshfree method for the numerical solution of the RLW equation. J Comput Appl Math. 2009;223:997–1012. doi: 10.1016/j.cam.2008.03.039
  • Mokhtari R, Ziaratgahi ST. Numerical solution of RLW equation using integrated radial basis functions. Appl Comput Math. 2011;10(3):428–448.
  • Mei L, Chen Y. Numerical solutions of RLW equation using Galerkin method with extrapolation techniques. Comput Phys Commun. 2012;183:1609–1616. doi: 10.1016/j.cpc.2012.02.029
  • Hammad DA, El-Azab MS. A 2N order compact finite difference method for solving the generalized regularized long wave (GRLW) equation. Appl Math Comput. 2015;253:248–261.
  • Yagmurlu NM, Ucar Y, Celikkaya I. Operator splitting for numerical solutions of the RLW equation. J Appl Anal Comput. 2018;8(5):1494–1510.
  • Omrani K, Abidi F, Achouri T, et al. A new conservative finite difference scheme for the Rosenau equation. Appl Math Comput. 2008;201:35–43.
  • Wang M, Li D, Cui P. A conservative finite difference scheme for the generalized Rosenau equation. Int J Pure Appl Math. 2011;71(4):539–549.
  • Toscani G. A Rosenau-type approach to the approximation of the linear Fokker-Planck equation. Kinet Relat Mod. 2018;11:697–714. doi: 10.3934/krm.2018028
  • Wongsaijai B, Poochinapan K. A three-level average implicit finite difference scheme to solve equation obtained by coupling the Rosenau-KdV equation and the Rosenau-RLW equation. Appl Math Comput. 2014;245:289–304.
  • Apolinar-Fernandez A, Ramos JI. Numerical solution of the generalized, dissipative KdV-RLW-Rosenau equation with a compact method. Commun Nonlinear Sci. 2018;60:165–183. doi: 10.1016/j.cnsns.2018.01.010
  • Wongsaijai B, Mouktonglang T, Sukantamala N, et al. Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation. Appl Math Comput. 2019;340:84–100.
  • Xie J, Zhang Z. An analysis of implicit conservative difference solver for fractional Klein–Gordon–Zakharov system. Appl Math Comput. 2019;348:153–166.
  • Korteweg D, de-Vries G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos Mag. 1895;39:422–443. doi: 10.1080/14786449508620739
  • Hu J, Wang Y. A high accuracy linear conservative difference scheme for Rosenau-RLW equation. Math Probl Eng. 2013;2013:1–8. Article ID 870291..
  • Rosenau P. Dynamics of dense discrete systems: High order effects. Progr Theor Phys. 1988;79(5):1028–1042. doi: 10.1143/PTP.79.1028
  • Xue G-Y, Zhang L. A new finite difference scheme for generalized Rosenau–Burgers equation. Appl Math Comput. 2013;222:490–496.
  • Peregrine DH. Calculation of the development of an undular bore. J Fluid Mech. 1966;25(2):321–330. doi: 10.1017/S0022112066001678
  • Omrani K. The convergence of the fully discrete Galerkin approximations for the Benjiamin–Bona–Mahony (BBM) equation. Appl Math Comput. 2006;180:614–621.
  • Chegini NJ, Salaripanah A, Mokhtari R, et al. Numerical solution of the regularized long wave equation using nonpolynomial splines. Nonlinear Dyn. 2012;69:459–471. doi: 10.1007/s11071-011-0277-y
  • Abbaszadeh M, Dehghan M. The two-grid interpolating element free Galerkin (TG-IEFG) method for solving Rosenau-regularized long wave (RRLW) equation with error analysis. Appl Anal. 2018;97:1129–1153. doi: 10.1080/00036811.2017.1303137
  • Li S. Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations. Numer Methods Partial Differ Eq. 2019;35:60–83. doi: 10.1002/num.22285
  • Yan J, Lai M-C, Li Z, et al. New conservative finite volume element schemes for the modified regularized long wave equation. Adv Appl Math Mech. 2017;9:250–271. doi: 10.4208/aamm.2014.m888
  • Pan X, Zhang L. On the convergence of a conservative numerical scheme for the usual Rosenau-RLW equation. Appl Math Model. 2012;36:3371–3378. doi: 10.1016/j.apm.2011.08.022
  • Coclite GM, Ruvo L. On the convergence of the modified Rosenau and the modified Benjamin–Bona–Mahony equations. Comput Math Appl. 2017;74:899–919. doi: 10.1016/j.camwa.2016.02.016
  • Wang X, Dai W. A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau–Kawahara-RLW equation. Comput Appl Math. 2018;37:6560–6581. doi: 10.1007/s40314-018-0685-4
  • Wongsaijai B, Poochinapan K, Disyadej T. A compact finite difference method for solving the general Rosenau-RLW equation. Int J Appl Math. 2014;44:192–199.
  • Wang H, Li S, Wang J. A conservative weighted finite difference scheme for the generalized Rosenau-RLW equation. Comput Appl Math. 2017;36:63–78. doi: 10.1007/s40314-015-0214-7
  • Ghiloufi A, Kadri T. Analysis of new conservative difference scheme for two-dimensional Rosenau-RLW equation. Appl Anal. 2017;96:1255–1267. doi: 10.1080/00036811.2016.1186270
  • Atouani N, Omrani K. On the convergence of conservative difference schemes for the 2D generalized Rosenau–Korteweg de Vries equation. Appl Math Comput. 2015;250:832–847.
  • He D, Pan K. A linearly implicit conservative difference scheme for the generalized Rosenau–Kawahara-RLW equation. Appl Math Comput. 2015;271:323–336.
  • Cai W, Sun Y, Wang Y. Variational discretizations for the generalized Rosenau-type equations. Appl Math Comput. 2015;271:860–873.
  • Ran M, Zhang C. New compact difference scheme for solving the fourth-order time fractional sub-diffusion equation of the distributed order. Appl Numer Math. 2018;129:58–70. doi: 10.1016/j.apnum.2018.03.005
  • Wang X, Dai W, Guo S. A conservative linear difference scheme for the 2D regularized long-wave equation. Appl Math Comput. 2019;342:55–70.
  • Liao H-L, Sun Z-Z. Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations. Numer Methods Partial Differ Eq. 2010;26(1):37–60. doi: 10.1002/num.20414
  • Ghiloufi A, Omrani K. New conservative difference schemes with fourth-order accuracy for some model equation for nonlinear dispersive waves. Numer Methods Partial Differ Eq. 2018;34:451–500. doi: 10.1002/num.22208

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