非齐次边界条件Rosenau-KdV方程的有限差分格式  

Finite Difference Scheme for the Rosenau-KdV Equation with Inhomogeneous Boundary Conditions

作　　者：刘佳垚 王晓峰 罗诗栋 LIU Jia-yao;WANG Xiao-feng;LUO Shi-dong(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,Fujian,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：《喀什大学学报》2023年第6期13-17,共5页Journal of Kashi University

基　　金：福建省自然科学基金项目“几类非线性发展方程高精度算法设计与应用研究”(2020J01796).

摘　　要：通过辅助函数的构造,将Rosenau-KdV方程的非齐次边界转化为齐次边界,并对齐次边界问题构造三层二阶线性差分格式;通过离散能量法和Von Neumann稳定性分析法分别证明了数值解的唯一性和无条件稳定性.数值算例验证了构建的差分格式的精度和可行性.Through the construction of auxiliary functions,the inhomogeneous boundary of the Rosenau-KdV equation is transformed into a homogeneous boundary,and a three-level second-order linear difference scheme is constructed for the homogeneous boundary problem.The uniqueness and unconditional stability of the numerical solution are proved by the discrete energy method and the von Neumann stability analysis method,respectively.Numerical examples are given to verify the accuracy and feasibility of the constructed difference scheme.

关 键 词：Rosenau-KdV方程 差分格式 非齐次边界 无条件稳定性 

分 类 号：O241.82[理学—计算数学]