Uniform error estimates of fourth-order conservative linearized difference scheme for a mathematical model for long wave

References

• T. Achouri and K. Omrani, Application of the homotopy perturbation method to the modified regularized long-wave equation, Numer. Methods Partial Differ. Equ. 26(2) (2010), pp. 399–411.
   Web of Science ®Google Scholar
• T. Achouri, N. Khiari, and K. Omrani, On the convergence of difference schemes for the Benjamin–Bona–Mahony (BBM) equation, Appl. Math. Comput. 182(2) (2006), pp. 999–1005.
   Web of Science ®Google Scholar
• T.B. Benjamin, J.L. Bona, and J.J. Mahony, Model equations for long waves in non-linear dispersive systems, Philos. Trans. R. Soc. Lond. Ser. A 272 (1972), pp. 47–78. doi: 10.1098/rsta.1972.0032
   Web of Science ®Google Scholar
• G. Berikelashvili and M. Mirianashvili, A one-parameter family of difference schemes for the regularized long-wave equation, Georgian Math. J. 18 (2011), pp. 639–667. doi: 10.1515/GMJ.2011.0044
   Web of Science ®Google Scholar
• I. Dag and M.N. Özer, Approximation of the RLW equation by the least square cubic B-spline finite element method, Appl. Math. Model. 25 (2001), pp. 221–231. doi: 10.1016/S0307-904X(00)00030-5
   Web of Science ®Google Scholar
• M. Dehghan and R. Salehi, The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas, Comput. Phys. Commun. 182(12) (2011), pp. 2540–2549. doi: 10.1016/j.cpc.2011.07.018
   Web of Science ®Google Scholar
• M. Dehghan, M. Abbaszadeh, and A. Mohebbi, The numerical solution of nonlinear high dimensional generalized Benjamin–Bona–Mahony–Burgers equation via the meshless method of radial basis functions, Comput. Math. Appl. 68 (2014), pp. 212–237. doi: 10.1016/j.camwa.2014.05.019
   Web of Science ®Google Scholar
• M. Dehghan, M. Abbaszadeh, and A. Mohebbi, The use of interpolating element-free Galerkin technique for solving 2D generalized Benjamin-Bona–Mahony–Burgers and regularized long-wave equations on non-rectangular domains with error estimate, J. Comput. Appl. Math. 286 (2015), pp. 211–231. doi: 10.1016/j.cam.2015.03.012
   Web of Science ®Google Scholar
• A. Dogan, Petrov–Galerkin finite element methods, Thesis Phil. Doct., 1997.
   Google Scholar
• L.R.T. Gardner, G.A. Gardner, F.A. Ayoub, and N.K. Amein, Approximations of solitary waves of the MRLW equation by B-spline finite element, Arab. J. Sci. Eng. 22 (1997), pp. 183–193.
   Web of Science ®Google Scholar
• A. Ghiloufi and T. Kadri, Analysis of new conservative difference scheme for two-dimensional Rosenau-RLW equation, Appl. Anal. 2016. DOI:10.1080/00036811.2016.1186270.
   PubMed Web of Science ®Google Scholar
• A. Ghiloufi, A. Rouatbi, and K. Omrani, A new conservative fourth order accurate difference scheme for solving of a model of nonlinear dispersive equations, Math. Methods Appl. Sci. 41 (2018), pp. 5230–5253. doi: 10.1002/mma.5073
   Web of Science ®Google Scholar
• B.Y. Guo and W.M. Cao, The Fourier pseudospectral method with a restrain operator for the RLW equation, J. Comput. Phys. 74(1) (1988), pp. 110–126. doi: 10.1016/0021-9991(88)90072-1
   Web of Science ®Google Scholar
• D. He, 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 Dyn. 2016. DOI:10.1007/s11071-016-2700-x.
   Web of Science ®Google Scholar
• D. He and K. Pan, A linearly implicit conservative difference scheme for the generalized Rosenau–Kawahara-RLW equation, Appl. Math. Comput. 271 (2015), pp. 323–336.
   Web of Science ®Google Scholar
• S.U. Islam, S. Haq, and A. Ali, A meshfree method for the numerical solution of the RLW equation, J. Comput. Appl. Math. 223(2) (2009), pp. 997–1012. doi: 10.1016/j.cam.2008.03.039
   Web of Science ®Google Scholar
• A.K. Khalifa, K.R. Raslan, and H.M. Alzubaidi, A finite difference scheme for the MRLW and solitary wave interactions, Appl. Math. Comput. 189 (2007), pp. 346–354.
   Web of Science ®Google Scholar
• A.K. Khalifa, K.R. Raslan, and H.M. Alzubidi, A collocation method with cubic B-splines for solving the MRLW equation, Appl. Math. Comput. 212 (2008), pp. 406–418. doi: 10.1016/j.cam.2006.12.029
   Web of Science ®Google Scholar
• S. Kutluay and A. Esen, A finite difference solution of the regularized long-wave equation, Math. Prob. Eng. 2006 (2006), pp. 1–14. doi: 10.1155/MPE/2006/85743
   Web of Science ®Google Scholar
• R. Mokhtari and M. Mohammadi, Numerical solution of GRLW equation using Sinc-collocation method, Comput. Phys. Commun. 181(7) (2010), pp. 1266–1274. doi: 10.1016/j.cpc.2010.03.015
   Web of Science ®Google Scholar
• K. Omrani and M. Ayadi, Finite difference discretization of the Benjamin–Bona–Mahony–Burgers equation, Numer. Methods Partial Differ. Equ. 24(1) (2008), pp. 239–248. doi: 10.1002/num.20256
   Web of Science ®Google Scholar
• D.H. Peregrine, Calculations of the development of an undular bore, J. Fluid Mech. 25 (1966), pp. 321–330. doi: 10.1017/S0022112066001678
   Web of Science ®Google Scholar
• A. Rashid, A three levels finite difference method for the nonlinear regularized long wave equation, Mem. Differ. Equ. Math. Phys. 34 (2005), pp. 135–146.
   Google Scholar
• K.R. Raslan, A computational method for the regularized long wave (RLW) equation, Appl. Math. Comput. 167(2) (2005), pp. 1101–1118.
   Web of Science ®Google Scholar
• A. Rouatbi and K. Omrani, Two conservative difference schemes for a model of nonlinear dispersive equations, Chaos Solitons Fractals 104 (2017), pp. 516–530. doi: 10.1016/j.chaos.2017.09.006
   Web of Science ®Google Scholar
• A. Rouatbi, T. Achouri, and K. Omrani, High-order conservative difference scheme for a model of nonlinear dispersive equations, Comput. Appl. Math. 2018. DOI:10.1007/s40314-017-0567-1.
   Google Scholar
• A. Shokri and M. Dehghan, A meshless method using the radial basis functions for numerical solution of the regularized long wave equation, Numer. Methods Partial Differ. Equ. 26(4) (2010), pp. 807–825.
   Web of Science ®Google Scholar
• T. Wang, L. Zhang, and F. Chen, Conservative schemes for the symmetric regularized long wave equations, Appl. Math. Comput. 190 (2007), pp. 1063–1080.
   Web of Science ®Google Scholar
• S.U.Y. Zhou, Application of Discrete Functional Analysis to the Finite Difference Methods, International Academic Publishers, Beijing, 1990.
   Google Scholar