Paper Info
Title
Study on the dynamics of a nonlinear dispersion model in both 1D and 2D based on the fourth-order compact conservative difference scheme
Abstract
In this paper, the nonlinear dispersion wave model in both 1D and 2D is studied by the compact finite difference method, which is called the generalized Rosenau–RLW equation. A fourth-order compact three-level and linearized difference scheme that maintains the original conservative properties of equation is proposed. The discrete mass conservation and discrete energy conservation of compact difference scheme are obtained. The solvability of numerical scheme is obtained. By using the discrete energy method, convergence and unconditional stability can also be obtained without relying on the grid ratio, and the optimal error estimates in the L∞ norm are fourth-order and second-order accuracy for the spatial and temporal step sizes, respectively. The scheme is conservative so can be used for long time computation. Numerical experiment results show that the theory is accurate and the method is efficient and reliable. Finally, the new numerical scheme is used to study the nonlinear dynamic of 1D generalized Rosenau–RLW equation and the wave interference of 2D generalized Rosenau–RLW equation, focusing on the influence of nonlinear convection term on the wave and the conservation of wave propagation.
Year
DOI
Venue
2021
10.1016/j.matcom.2020.11.012
Mathematics and Computers in Simulation
Keywords
DocType
Volume
Generalized Rosenau–RLW equation,Conservation law,Compact difference scheme,Unconditional stability and convergence,Nonlinear dynamic
Journal
182
ISSN
Citations 
PageRank 
0378-4754
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Yu.I. Dimitrienko100.34
Shuguang Li252.52
Yi Niu34619.65