重心插值配点法求解小振幅长波广义BBM-KdV方程  

Barycentric interpolation collocation method for solving the small-amplitude long-wave scheme generalized BBM-KdV equation

作　　者：吕秀敏 葛倩[2] 李金[2] Xiumin LYU;Qian GE;Jin LI(School of Science,Shandong Jiaotong University,Jinan 250357,Shandong,China;School of Science,Shandong Jianzhu University,Jinan 250101,Shandong,China)

机构地区：[1]山东交通学院理学院,山东济南250357 [2]山东建筑大学理学院,山东济南250101

出　　处：《山东大学学报（理学版）》2024年第8期67-76,共10页Journal of Shandong University(Natural Science)

基　　金：山东省自然科学基金资助项目(ZR2022MA003);山东交通学院科研基金资助项目(Z202334)

摘　　要：应用重心插值配点法求解小振幅长波格式下的广义Benjamin-Bona-Mahony(BBM)-Korteweg-de Vries(KdV)方程。针对方程中的非线性项ηpηx,采用直接线性化方法将其转化为线性项。利用重心插值基函数构造方程未知函数的近似函数,建立时空域上重心插值配点法离散广义BBM-KdV方程的矩阵方程,并进行了收敛性分析。数值算例验证了重心插值配点法求解广义BBM-KdV方程的有效性和数值计算精度,其计算精度可达到10-8量级。The barycentric interpolation collocation method is applied to solve the small-amplitude long-wave scheme generalized Benjamin-Bona-Mahony(BBM)-Korteweg-de Vries(KdV)equation in the small amplitude long wave scheme.By the direct linearization method,the nonlinear termηpηx in the equation is converted into a linear term.Unknown functions of BBM-KdV equation is approximated by the barycentric interpolation basis function.The matrix equation of the generalized BBM-KdV equation is obtained by discretized the generalized BBM-KdV equation in the space-time domain,and the convergence analysis is carried out.The effectiveness and numerical accuracy of the barycentric interpolation collocation method is verified by numerical example,and the calculation accuracy can reach the order of 10-8.

关 键 词：小振幅长波 广义BBM-KdV方程 重心插值 配点法 

分 类 号：O241[理学—计算数学]