一维线性Klein-Gordon方程Neumann边值问题的高阶差分格式  

A HIGH ORDER ACCURACY DIFFERENCE SCHEME FOR THE NONLINEARKLEIN-GORDON EQUATION WITH NEUMANN BOUNDARY CONDITIONS

作　　者：盛秀兰 郝宗艳[1] 吴宏伟 SHENG Xiu-lan;HAO Zong-yan;WU Hong-wei(School of Mathematics, Southeast University, Nanjing 210096, China;School of General Education, Jiangsu Open University, Nanjing 210036, China)

机构地区：[1]东南大学数学学院,江苏南京210096 [2]江苏开放大学通识教育学院,江苏南京210036

出　　处：《数学杂志》2019年第1期77-86,共10页Journal of Mathematics

基　　金：国家自然科学基金(11671081);江苏开放大学"十三五"规划课题(16SSW-Y-009)

摘　　要：本文主要研究非线性Klein-Gordon方程Neumann边值问题的高阶差分格式.利用边界条件及非线性Klein-Gordon方程,得到其在空间上的三阶与五阶导数的边界值,进而分别在内点和边界点建立三点和两点紧差分格式.借助能量估计、Gronwall和Schwarz不等式、数学归纳法等技巧进行分析,得到截断误差是关于时间和空间上的二阶和四阶收敛.通过理论分析差分格式的收敛性和稳定性以及数值算例,验证了理论分析结果.This paper is devoted to the study of high-order accuracy difference methods for the Klein-Gordon equation with Neumann boundary conditions. By using the boundary values of three-order and five-order derivatives, the three points scheme at inside points and two points scheme at boundary points are established respectively. The truncation error of difference scheme is second order in time and fourth order in space. Convergence and stability of difference scheme are analyzed by using energy estimate. Numerical results are conducted to illustrate the theoretical results of the presented scheme in this paper.

关 键 词：非线性KLEIN-GORDON方程 紧差分格式 收敛性 稳定性 高精度 

分 类 号：O241.82[理学—计算数学]