KdV方程的保能量组合高阶紧致格式  

COMBINED HIGH ORDER COMPACT ENERGY-PRESERVING SCHEME FOR KDV EQUATION

作　　者：王剑东 孔令华 许巧梦 郭花城 Wang Jiandong;Kong Linghua;Xu Qiaomeng;Guo Huacheng(School of Mathematics and Statistics,Jiangci Normal University,Nanchang 330022,China;Jiangri Provincial Center for Applied Mathematics,Nanchang 330022,China)

机构地区：[1]江西师范大学数学与统计学院,南昌昌330022 [2]江西省应用数学中心,南昌330022

出　　处：《数值计算与计算机应用》2024年第3期273-287,共15页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金项目(11961036,12361075);江西省自然科学基金项目(20224ACB201001,20224BCD41001)资助.

摘　　要：本文为KdV方程设计了一个组合高阶紧致方法,该方法同时紧致地计算了一阶和三阶空间导数,克服了传统高阶紧致方法的许多不足。对KdV方程在空间上采用组合高阶紧致格式离散,时间上用Crank-Nicolson格式并结合外推方法进行逼近,同时利用投影方法以得到一个全离散保能量格式.最后,数值实验验证了格式的收敛精度、计算效率和保能量性态.It designs a combined high-order compact method for KdV equation in this work.This method simultaneously and compactly calculates the first-order and third-order spa-tial derivatives which overcomes many shortcomings of classic high-order compact methods.The KdV equation is discretized by the combined high-order compact method in space,and is approximated by the Crank-Nicolson scheme combined with extrapolation method in time.In addition,projection method is used to pull the numerical solution back to the energy-preserving manifold.Finally,some numerical experiments are conducted to verify the numerical accuracy,computational efficiency,and the property of energy-preserving.

关 键 词：KDV方程 组合高阶紧致格式 保能量格式 投影方法 

分 类 号：O241.82[理学—计算数学]