指标1积分代数方程在连续分段多项式空间的配置方法的收敛性  

On the convergence of collocation methods in continuous piecewise polynomial spaces for integral-algebraic equations of index 1

作　　者：张婷婷 张宇佳 梁慧[1] ZHANG Tingting;ZHANG Yujia;LIANG Hui(College of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院

出　　处：《黑龙江大学自然科学学报》2019年第5期505-514,共10页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Research Fund of the Heilongjiang Provincial Education Department for the Academic Backbone of the Excellent Young People(1254G044)

摘　　要：采用连续分段多项式空间配置方法求解指标1的积分代数方程。给出在连续分段多项式空间的配置格式,证明该配置解的存在唯一性。对cm=1,详尽地分析在连续的分段多项式空间配置方法的收敛条件;根据收敛条件的不同,采用不同的技巧,得到相应的收敛阶。数值算例验证了理论分析的正确性。The collocation method in continuous piecewise polynomial spaces is applied to solve integral-algebraic equations of index 1.The collocation scheme in continuous piecewise polynomial spaces is shown,and the existence and uniqueness of the collocation solutions are proved.For c m=1,the convergence condition of the collocation method in continuous piecewise polynomial spaces is analyzed in detail and different techniques are used to obtain corresponding convergence order according to the different convergence conditions.Some numerical experiments are given to illustrate theoretical analysis.

关 键 词：积分代数方程 配置方法 连续分段多项式空间 收敛性 

分 类 号：O241.83[理学—计算数学]