半直线上积分方程逼近解  

Approximate solution of the integral equation on the half line

作　　者：邸继征[1] 石智慧[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310032

出　　处：《浙江工业大学学报》2009年第3期326-331,共6页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(60874122)

摘　　要：针对许多应用问题中,核函数性质不好,精确解不能得到,须考虑逼近解的情况,讨论半直线上积分方程的逼近解.对定义于L2[0,∞)的积分算子,给出截断算子的定义,赋予核函数简洁的条件,证明了相应积分算子的有界性、正则性和截断算子的紧性,得到截断逼近定理.在此基础上研究L2范数下半直线上积分方程的逼近解,得到解的逼近方式,建立了逼近估计定理.对于特殊类型的方程,得到了幂型和指数型逼近估计.从实例看出,对一类积分方程,逼近解的效果十分理想.For many questions, because properties of the kernel function are not good, we can＇t get the accurate solutions. In this paper, we study the approximate solution of the integral equation on the half line. Firstly, the truncation operator is defined under simple and convenient conditions on the kernel function of the integral operator, then its properties are studied and an operator approximation theorem is given. Secondly the approximate solutions of such equations are given and the approximate estimations are studied, then for a kind of integral equations of power-type and exponential approximate estimations are obtained. Lastly an example shows that the effects of such approximations are good.

关 键 词：积分方程 积分算子 逼近解 

分 类 号：O175.5[理学—数学]