The conservative and fourth-order compact finite difference schemes for regularized long wave equation

被引：30
作者：
Wang, Bo [1 ,3 ]
Sun, Tongjun [1 ]
Liang, Dong [2 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada
[3] Civil Aviat Univ China, Dept Math, Coll Sci, Tianjin 300300, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 356卷
基金：
中国国家自然科学基金; 加拿大自然科学与工程研究理事会;
关键词：
RLW equation; Compact finite difference; Conservation; Stability; Convergence; NUMERICAL-SOLUTION; PSEUDOSPECTRAL METHOD; GALERKIN METHOD; ELEMENT METHODS; CONVERGENCE;
D O I：
10.1016/j.cam.2019.01.036
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
引用
收藏
页码：98 / 117
页数：20
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