一种通用六阶紧致差分格式在耦合Schrodinger-KdV方程中的应用  

A General Sixth-order Compact Finite Difference Scheme for Coupled Schrodinger-KdV Equations

作　　者：仇佳栋 梁琪琪 胡志涛 韩丹夫 QIU Jiadong;LIANG Qiqi;HU Zhitao;HAN Danfu(School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China)

机构地区：[1]杭州师范大学数学学院,浙江杭州311121

出　　处：《杭州师范大学学报（自然科学版）》2022年第6期631-639,共9页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11471092)。

摘　　要：构造了一种六阶紧致差分格式的通用矩阵形式,并将其应用于耦合Schrodinger-KdV方程的数值求解,证明了物理不变量在该格式下的守恒性.数值实验表明所用方法具有较好的不变量守恒性,并较其他数值计算方法具有更高的收敛阶.In this paper, a general matrix form of sixth-order compact finite difference scheme was constructed and applied to solve the coupled Schrodinger-KdV equations numerically. The proposed scheme was proved to preserve several given invariants. Numerical experiments showed that the proposed method well preserved the given invariants and had higher accuracy than other numerical methods.

关 键 词：耦合Schrodinger-KdV方程 紧致差分格式 循环边界条件 守恒性 

分 类 号：O241.82[理学—计算数学]