期刊导航

论文摘要

耗散SRLW方程的拟紧致非线性有限差分逼近

Pseudo compact nonlinear finite difference approximate solution for dissipative symmetric regularized long wave equation

作者:郑茂波(成都工业学院);胡兵(四川大学数学学院)

Author:ZHENG Mao-Bo(Chengdu Technological University);HU Bing(College of Mathematics, Sichuan University)

收稿日期:2013-06-13          年卷(期)页码:2015,52(4):715-720

期刊名称:四川大学学报: 自然科学版

Journal Name:Journal of Sichuan University (Natural Science Edition)

关键字:耗散对称正则长波方程; 差分格式; 收敛性; 稳定性

Key words:Dissipative symmetric regularized long wave equation; Finite difference scheme; Convergence; Stability

基金项目:四川省教育厅青年基金项目(11ZB009);成都工业学院项目(KY1211007B)

中文摘要

本文对具有耗散项的对称正则长波(SRLW)方程的初边值问题进行了数值研究,提出了一个两层隐式拟紧致差分格式,该格式合理地模拟了问题本身的两个守恒律,得到了差分解的存在唯一性,并在差分解的先验估计的基础上用能量方法分析了该格式的二阶收敛性与无条件稳定性.数值结果表明该格式的精度明显优于一般的二阶格式.

英文摘要

An implicit pseudo compact two level scheme is proposed for the initial value problems of dissipative symmetric regularized long wave equation. The scheme simulates two conservation properties of the problem well. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, second order convergence and unconditionally stability are discussed.Numerical examples show that the accuracy of the scheme is much better than the general second order scheme.

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