General Improved KdV方程的三层加权平均线性差分格式
Three-level average linear difference scheme for the general improved KdV equation
作者：赵红伟(四川大学数学学院)；胡兵(四川大学数学学院)；郑茂波(成都工业学院)
Author：ZHAO Hong-Wei(College of Mathematics, Sichuan University)；Hu Bing(College of Mathematics, Sichuan University)；ZHENG Mao-Bo(Chengdu Technological University)
收稿日期：2016-04-11 年卷（期）页码：2017,54(1):12-18
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：GIKdV方程, 线性差分格式, 收敛性, 稳定性
Key words：GIKdV equation, linear difference scheme, convergence, stability
基金项目：
中文摘要
论文对广义improved KdV方程的初边值问题进行了数值研究, 提出了一个三层加权平均线性差分格式, 分析了差分解的存在唯一性, 证明了格式的二阶收敛性和稳定性, 数值试验验证了差分格式的有效性.
英文摘要
In this paper, a numerical method for an initial-boundary value problem of the general Improved KdV equation is considered. A three-level average linear-implicit finite difference scheme is proposed and the existence and uniqueness are discussed. It is shown that the finite difference scheme is of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.
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