一类Fredholm-Hammerstein型泛函积分方程不动点迭代与Aitken加速迭代算法  

Fixed Point Iteration and Aitkin Acceleration Iteration for a Class of Fredholm-Hammerstein functional integral equations

作　　者：刘子灵 王奇生[1] 

机构地区：[1]五邑大学数学与计算科学学院,广东江门529020

出　　处：《五邑大学学报（自然科学版）》2018年第1期13-18,共6页Journal of Wuyi University(Natural Science Edition)

基　　金：广东省自然科学基金资助项目(2015A030313643;2016A030313005);广东省普通高校创新强校特色创新项目(2015KTSCX147)

摘　　要：利用Banach不动点原理,给出了一类Fredholm-Hammerstein型非线性泛函积分方程解析解的存在唯一性定理.分别给出了不动点迭代与Aitken加速迭代的数值算法、误差估计、收敛性分析.最后通过两个数值例子验证了收敛性定理的有效性,并得到两种算法的比较分析结果.In this paper, the existence and uniqueness of a class of Fredholm-Hammerstein functional integral equations are first given by using the Banach fixed point theorem. Secondly, the numerical algorithm of fixed point iteration and Aitkin acceleration iteration are presented. Moreover, the error estimation and convergence analysis are obtained. Finally, efficiency of convergence theorem is validated by using two numerical examples, and furthermore the comparative analysis result of these two algorithms is also got.

关 键 词：Fredholm-Hammerstein型泛函积分方程 不动点迭代 Aitken加速迭代 误差估计 收敛性分析 

分 类 号：O189.1[理学—数学]