References
- Rosenau P. A quasi-continuous description of a nonlinear transmission line. Phys Scripta. 1986;34:827–829. doi: 10.1088/0031-8949/34/6B/020
- Rosenau P. Dynamics of dense discrete systems. Progr Theor Phys. 1988;79:1028–1042. doi: 10.1143/PTP.79.1028
- Park MA. On the Rosenau equation. Math Appl Comput. 1990;9:145–152.
- Chung SK. Finite difference approximate solutions for the Rosenau equation. Appl Anal. 1998;69:149–156. doi: 10.1080/00036819808840652
- Manickam SA, Pani AK, Chung SK. A second order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation. Numer Methods Partial Differential Equations. 1998;14:695–716. doi: 10.1002/(SICI)1098-2426(199811)14:6<695::AID-NUM1>3.0.CO;2-L
- Kim YD, Lee HY. The convergence of finite element Galerkin solution for the Rosenau equation. Korean J Comput Appl Math. 1998;5:171–180.
- Chung SK, Pani AK. Numerical methods for the Rosenau equation. Appl Anal. 2001;77:351–369. doi: 10.1080/00036810108840914
- Liu L, Mei M, Wong YS. Asymptotic behavior of solutions to the Rosenau–Bergers equation with a periodic initial boundary. Nonlinear Anal. 2007;67:2527–2539. doi: 10.1016/j.na.2006.08.047
- Liu L, Mei M. A better asymptotic profile of Rosenau–Burgers equation. Appl Math Comput. 2002;131:147–170.
- Mei M. Long-time behavior of solution for Rosenau–Burgers equation (I). Appl Anal. 1996;63:315–330. doi: 10.1080/00036819608840511
- Mei M. Long-time behavior of solution for Rosenau–Burgers equation (II). Appl Anal. 1998;68:333–356. doi: 10.1080/00036819808840635
- Lopez-Marcos M. Numerical analysis of pseudospectral methods for the Kuramoto–Sivashinsky equation. IMA J Numer Anal. 1994;14(2):233–242. doi: 10.1093/imanum/14.2.233
- Akrivis D. Finite difference discretization of the Kuramoto–Sivashinsky equation. Numer Math. 1992; 63(1):1–11. doi: 10.1007/BF01385844
- Khater A, Temsah R. Numerical solutions of the generalized Kuramoto–Sivashinsky equation by Chebyshev spectral collocation methods. Comput Math Appl. 2008;56(6):1465–1472. doi: 10.1016/j.camwa.2008.03.013
- Kinami S, Mei M, Omata S. Convergence to diffusion waves of the solutions for Benjamin–Bona–Mahony–Burgers equations. Appl Anal. 2000;75(3–4):317–340. doi: 10.1080/00036810008840852
- Al-Khaled K, Momani S, Alawneh A. Approximate wave solutions for the generalized for Benjamin–Bona–Mahony–Burgers equations. Appl Math Comput. 2005;171(1):281–292.
- Hasan MT, Xu C. Numerical approximation for MHD flows of generalized viscoelastic fluid. Appl Anal. 2017:1–19. doi: 10.1080/00036811.2017.1397638
- Pan X, Zhang L. A new finite difference scheme for the Rosenau–Burgers equation. Appl Math Comput. 2012;218:8917–8924.
- Hu B, Xu Y, Hu J. Crank-Nicolson finite difference scheme for the Rosenau–Burgers equation. Appl Math Comput. 2008;204:311–316.
- Adams RA. Sobolev spaces. New York, San Francisco, London: Academic Press; 1975.
- Bernardi C, Maday Y. Spectral methods. In: Ciarlet PG, Lions JL, editors. Handbook of numerical analysis. Amsterdam: Elsevier; 1997, p. 333–365.
- Quarteroni A, Valli A. Numerical approximation of the partial differential equations. Berlin: Springer-Verlag; 1994.