谱配置法求解常微分方程初值问题的超收敛性  

Superconvergence of spectral collocation method for initial value problem of ordinary differential equations

作　　者：钱轶昀 查媛媛 蔡康文 刘艳勤 王心怡 易利军[1] QIAN Yiyun;ZHA Yuanyuan;CAI Kangwen;LIU Yanqin;WANG Xinyi;YI Lijun(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2021年第1期1-7,共7页Journal of Shanghai Normal University(Natural Sciences)

基　　金：上海师范大学“大学生创新创业训练计划”资助项目。

摘　　要：研究了常微分方程初值问题的谱配置方法.针对一阶和二阶线性常微分方程初值问题,基于Legendre-Gauss点提出了相应的谱配置方法,并给出了具体的计算格式.最后,通过一些数值算例探讨了所提Legendre-Gauss谱配置方法的超收敛性.In this paper,we study the spectral collocation method for the initial value problems of ordinary differential equations.Based on Legendre-Gauss points,we propose the spectral collocation method for the initial value problems of first-order and second-order.We also give the specific computation form for our method.Finally,to explain the superconvergence properties of the Legendre-Gauss spectral collocation method.We discuss several numerical examples.

关 键 词：谱配置法 初值问题 超收敛 

分 类 号：O241.8[理学—计算数学]