Conservative finite difference scheme for the nonlinear fourth-order wave equation

被引：16
|
作者：
Achouri, Talha [1 ,2 ]
机构：
[1] Univ Sousse, Higher Inst Appl Sci & Technol Sousse, Ibn Khaldoun 4003, Sousse, Tunisia
[2] Shaqra Univ, Al Quwayiyah Coll Sci & Humanities, Dept Math, Al Quwayiyah 11971, Saudi Arabia
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 359卷
关键词：
Fourth-order wave equation; Difference scheme; Discrete energy; Existence; Uniqueness; Convergence; GLOBAL EXISTENCE; ASYMPTOTIC-BEHAVIOR; CAUCHY-PROBLEM; NONEXISTENCE; OSCILLATIONS; SCATTERING;
D O I：
10.1016/j.amc.2019.04.033
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A conservative finite difference scheme is presented for solving the two-dimensional fourth-order nonlinear wave equation. The existence of the numerical solution of the finite difference scheme is proved by Brouwer fixed point theorem. With the aid of the fact that the discrete energy is conserved, the finite difference solution is proved to be bounded in the discrete L-infinity-norm. Then, the difference solution is shown to be second order convergent in the discrete L-infinity-norm. A numerical example shows the efficiency of the proposed scheme. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：121 / 131
页数：11
相关论文
共 50 条
12345