| 使用直接离散化求解第一类Fredholm积分方程的误差估计 |
| |
| 引用本文： | 刘明辉. 使用直接离散化求解第一类Fredholm积分方程的误差估计[J]. 黑龙江大学自然科学学报, 2011, 28(1): 17-21 |
| |
| 作者姓名： | 刘明辉 |
| |
| 作者单位： | 吉林大学,数学研究所,长春,130012 |
| |
| 基金项目： | 国家自然科学基金资助项目 |
| |
| 摘 要： | 讨论一类存在唯一解的第一类Fredholm积分方程的直接离散化方法:复化梯形方法,复化Simpson方法,以及高斯法.从理论上给出了使用不同离散化方法求解该类积分方程的误差估计,特别给出了方程右端项有扰动时的误差界.数值实验表明高斯法在一定条件下具有很好的效果.
|
| 关 键 词： | 第一类Fredholm积分方程 离散化 不适定 |
Error estimate on direct discretization of Fredholm integral equation of the first kind |
| |
| LIU Ming-hui. Error estimate on direct discretization of Fredholm integral equation of the first kind[J]. Journal of Natural Science of Heilongjiang University, 2011, 28(1): 17-21 |
| |
| Authors: | LIU Ming-hui |
| |
| Affiliation: | LIU Ming-hui (Institute of Mathematics,Jilin University,Changchun 130012,China) |
| |
| Abstract: | Three direct discretization methods,including compound trapezoid method,compound Simpson method and Gauss method,are investigated for some Fredholm integral equation of the first kind,which has a unique solution.A theoretical analysis on error estimate is given on the direct discretization methods,especially on the case where there is a perturbation on the right-hand side.The numerical experiment indicates that Gauss method has a much better performance than the other two ones. |
| |
| Keywords: | Fredholm equation first kind direct discretization Ill-posed |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
