标题：The conservative and fourth-order compact finite difference schemes for regularized long wave equation
作者：Wang, Bo; Sun, Tongjun; Liang, Dong
作者机构：[Wang, Bo; Sun, Tongjun] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.; [Liang, Dong] York Univ, Dept Math & Stat, Toronto, ON M 更多
通讯作者：Sun, Tongjun;Sun, TJ
通讯作者地址：[Sun, TJ]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
关键词：RLW equation; Compact finite difference; Conservation; Stability;; Convergence
摘要：In this paper, two conservative and fourth-order compact finite difference schemes are proposed and analyzed for solving the regularized long wave (RLW) equation. The first compact finite difference scheme is two-level and nonlinear implicit. The second scheme is three-level and linearized implicit. Conservations of the discrete mass and energy, and unique solvability of the numerical solutions are proved. Convergence and unconditional stability are also derived without any restrictions on the grid ratios by using discrete energy method. The optimal error estimates in norm parallel to.parallel to and parallel to.parallel to L(infinity)are of fourth-order and second-order accuracy for the spatial and temporal step sizes, respectively. Numerical examples are presented to simulate the collision of different solitary waves and support the theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved.