二阶电报方程的一个新紧差分格式  

A New Compact Difference Scheme for Second-order Telegraph Equation

作　　者：李福乐[1] 秦墩旺 刘振斌[1] 徐英[1] LI Fule;QIN Dunwang;LIU Zhenbin;XU Ying(School of Science and Information Science,Qingdao Agricultural University,Qingdao 266109,China)

机构地区：[1]青岛农业大学理学与信息科学学院,山东青岛266109

出　　处：《青岛农业大学学报（自然科学版）》2022年第3期226-229,共4页Journal of Qingdao Agricultural University(Natural Science)

基　　金：青岛农业大学教学研究与课程改革重点项目(XJY2019035);教育部产学合作协同育人项目(201902040018);青岛农业大学教学研究项目(XJY2020030)。

摘　　要：考虑了一个二阶一维电报方程的高精度数值算法。利用有限差分法建立一个线性三层紧差分格式,用能量分析法证明紧差分格式解的唯一性、无条件稳定性和收敛性。使用数值实验验证理论结果和算法的有效性。A high-precision numerical algorithm for a second-order one-dimensional telegraph equation was considered.A linear three-level compact difference scheme for this problem was established by the finite difference method,and the uniqueness,unconditional stability and convergence of the solution of the compact difference scheme were proved by the energy analysis method.The theoretical results and the validity of the algorithm were verified using numerical experiments.

关 键 词：电报方程 紧差分格式 稳定性 

分 类 号：O241.82[理学—计算数学]