五阶KdV方程的高阶有限差分格式  

High-order Finite Difference Scheme for the Fifth-order KdV Equation

作　　者：石方圆 李书存[2] 奚茜[2] SHI Fangyuan LI Shucun XI Xi(College of Mathematics and Information Sciences,Hebei Normal University,Hebei Shijiazhuang 050024,China School of Applied Science,Beijing Information Science ＆ Technology Univcrsity,Beijing 100192,China)

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050024 [2]北京信息科技大学理学院,北京100192

出　　处：《河北师范大学学报（自然科学版）》2017年第2期104-110,共7页Journal of Hebei Normal University：Natural Science

摘　　要：利用Taylor展开法,分别给出了求解五阶KdV方程的九点四阶和七点二阶有限差分格式.前者在空间上具有四阶精度,在时间上具有二阶精度,后者具有时空二阶精度.数值算例将2个格式进行了比较并验证了格式的精度阶.此外,数值算例给出了2个单孤立波碰撞的情况.In this paper, we propose nine-point fourth-order finite difference scheme and a seven-point second-order finite difference scheme for the fifth-order KdV equation by using the Taylor expansion. The former scheme has fourth-order accuracy in space and second-order accuracy in time and the latter has second-order both in space and time. The nine-point fourth-order scheme and the seven-point second order scheme are compared by the numerical experiments and the numerical results verify the accuracy the claimed order for these schemes. We also analyze the phenomenon of binary co by a numerical example. lision of the solitary waves

关 键 词：五阶KDV方程 TAYLOR展开 有限差分 高阶格式 

分 类 号：O175.29[理学—数学]