非齐次边界条件KdV方程的有限差分格式  

A Finite Difference Scheme for KdV Equation with Inhomogeneous Boundaries

作　　者：邓雅清 王晓峰 程宏 何育宇 DENG Yaqing;WANG Xiaofeng;CHENG Hong;HE Yuyu(School of Mathematics and Statistics,Minnan Normal Univers My,Fujian Zhangzhou 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《河北师范大学学报（自然科学版）》2021年第2期112-118,共7页Journal of Hebei Normal University：Natural Science

基　　金：福建省自然科学基金(2020J01796)。

摘　　要：构造一个新的变量将KdV方程的非齐次边界转化为齐次边界,对于变换后的KdV初边值问题提出一个3层二阶精度线性有限差分格式.分别用离散能量法和von Neumann稳定性分析法证明了该格式解的唯一性和无条件稳定性.数值算例验证了该格式的精度和有效性.We construct a new variable to transform the KdV equation with the nonhomogeneous boundaries into the KdV equation with homogeneous boundaries,and propose a three-level second-order accurate linear finite difference scheme for the KdV equation with homogeneous boundaries.The discrete energy method and the von Neumann stability analysis method are used to prove the uniqueness and unconditional stability of the scheme,respectively.Numerical examples are provided to confirm that the scheme is accurate and efficient.

关 键 词：KDV方程 非齐次边界 有限差分格式 唯一解 无条件稳定 

分 类 号：O241.8[理学—计算数学]