带弱奇异核的第二类Fredholm积分方程数值解法比较  

Comparison of Numerical Solutions for the Second Kind Fredholm Integral Equation with Weakly Singular Kernel

作　　者：王丽丽[1] 王辉[1] 张欣[2] 

机构地区：[1]哈尔滨师范大学数学科学学院,黑龙江哈尔滨150025 [2]北京化工大学北方学院,河北三河065210

出　　处：《数学的实践与认识》2013年第22期184-188,共5页Mathematics in Practice and Theory

基　　金：黑龙江省教育厅科学技术研究项目(12521145)

摘　　要：针对带有弱奇异核的第二类Fredholm积分方程数值解法问题,介绍了两种方法.一种方法是泰勒级数展开法;另一种方法是将弱奇异核通过迭代变为连续核,再用L^1空间中的离散化方法求其数值解,且通过对具体算例作图分析,从而得出L^1空间中离散化方法更好.There are two kinds of methods to find the numerical solution for the second kind Fredholm integral equation with weakly singular kernel. One is the Taylor series expansion method. Another method is that we transform weakly singular kernel into continuous kernel, and then use the diseretization method for the numerical solution in L^1 space, and analysis a specific example by mapping to arrive at the discretization method from L^1 space is better.

关 键 词：FREDHOLM积分方程 弱奇异核 连续核 离散化方法 泰勒级数展开 误差估计 

分 类 号：O241.83[理学—计算数学]