论解第二类Volterra积分方程的Chebyshev极值点配置法  

On the Chebyshev Extreme Point Collocation Method for Solving the Second Type Volterra Integral Equation

作　　者：胡校颖 邱淑芳 HU Xiaoying;QIU Shufang(School of Science,East China University of Technology,330013,Nanchang,PRC;Department of Basic Courses,Guangzhou Maritime University,510725,Guangzhou,PRC)

机构地区：[1]东华理工大学理学院,南昌330013 [2]广州航海学院基础教学部,广州510725

出　　处：《江西科学》2024年第3期457-463,共7页Jiangxi Science

基　　金：国家自然科学基金项目(11961002,11861007);江西省自然科学基金重点项目(20212ACB201001);江西省研究生创新专项资金项目(YC2022-s617)。

摘　　要：讨论解第二类Volterra积分方程的一种Chebyshev极值点配置方法。介绍了Chebyshev多项式及其性质,阐述了Chebyshev极值点配置方法的构造思路及其计算步骤。研究了Chebyshev极值点配置方法的误差分析,给出了2种范数意义下数值解的误差估计。最后,数值实验说明,该方法求解第二类Volterra积分方程是有效的,且误差是收敛的。In this study,a Chebyshev extreme point collocation method for solving the second type Volterra integral equations is investigated.Recalls the basic definitions and some properties about the Chebyshev polynomials,also elaborates on the construction idea and specific calculation steps of the method.The error estimates of the numerical solutions of the method are obtained in terms of two kinds of norms.Finally,the numerical examples are provided to confirm the validity of the method for solving the second type Volterra integral equations,the convergence of the error.

关 键 词：VOLTERRA积分方程 CHEBYSHEV多项式 配置法 误差分析 数值积分 

分 类 号：O175.6[理学—数学]