Abel积分方程的数值解
Numerical Solution of Abel Integral Equation
刘雪铃 1黄静 1李明1
作者信息
- 1. 亳州学院 电子信息工程系,安徽 亳州 236800
- 折叠
摘要
文章研究了Abel积分方程的数值解.首先对Abel积分方程进行多次积分得到与之等价的积分方程,结合分段泰勒级数得到方程的数值解;然后利用Banach空间的映射原理,证明数值解的收敛性;最后通过例题验证此方法的可行性与有效性,并给相应的出误差估计.
Abstract
In order to obtain the numerical solution of Abel integral equation,the equivalent integral equation is obtained by multiple in-tegrations of Abel integral equation,and then the numerical solution of the equation is obtained by piecewise Taylor series.Then,the con-vergence and error estimate of the numerical solution are proved by using the mapping principle of Banach space.Finally,the feasibility and effectiveness of this method are demonstrated through corresponding examples,and corresponding error estimates are provided.
关键词
数值解/Abel积分方程/分段泰勒级数/收敛性/误差估计Key words
numerical solution/abelian integral equation/piecewise taylor-series expansion method/integral method/convergence and error estimation引用本文复制引用
基金项目
安徽省质量工程项目(2019mooc374)
安徽省教育厅自然科学研究重点项目(2022AH052415)
安徽省教学研究项目(2020jyxm1239)
安徽省教育厅自然科学研究项目(KJ2021A1150)
出版年
2024
NETL
NSTL
万方数据