基于重心插值配点的KdV方程无网格算法  

A meshless barycentric interpolation collocation method for numerical solution of KdV equation

作　　者：肖娜仁 XIAO Naren(School of Mathematics and Big Data,Hohhot Minzu College,Hohhot 010051,China)

机构地区：[1]呼和浩特民族学院数学与大数据学院,呼和浩特010051

出　　处：《内蒙古工业大学学报（自然科学版）》2022年第1期14-19,共6页Journal of Inner Mongolia University of Technology：Natural Science Edition

摘　　要：基于重心插值配点理论,为KdV方程构造了无网格算法.应用直接线性化与Newton-Raphson两种迭代格式对一类KdV方程进行数值求解,并与单孤立波形式及三孤立波形式解析解进行比较,计算了绝对误差和相对误差,对比了不同迭代的迭代次数,通过数值算例验证此数值方法对KdV方程求解具有高精度和有效性.Based on the barycenter interpolation collocation theory,a meshless method for solving the KdV equation is constructed.The direct linearized iteration method and Newton Raphson iterative schemes are used to solve the KdV equation,the absolute error and relative error are calculated by comparing with the single solitary wave and three solitary wave analytical solutions,and the iteration times of different iterations are compared.Numerical examples show that the numerical method has high precision and validity for solving the KdV equation.

关 键 词：KDV方程 重心插值配点 无网格 迭代格式 

分 类 号：O175.6[理学—数学]