二维第一类Fredholm积分方程数值解的RRGMRES算法  

RRGMRES method of numerical solution for Fredholm integral equations of the first kind in two dimensions

作　　者：闵涛[1] 党香燕 MIN Tao;DANG Xiangyan(School of Science,Xi’an University of Technology,Xi’an 710054,China)

机构地区：[1]西安理工大学理学院,西安710054

出　　处：《应用数学与计算数学学报》2018年第4期797-805,共9页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(51679186);青年科学基金资助项目(11601418)

摘　　要：利用数值积分将二维第一类Fredholm积分方程离散为一线性不适定问题,引入RRGMRES算法对得到的线性不适定问题求其数值解,给出了数值模拟,并与GMRES算法进行了分析比较,结果表明RRGMRES算法在求解此类问题时具有精度高抗干扰强的优点.The first kind of the two-dimensional Fredholm integral equation is discretized into a linear ill-posed problem by numerical integration,and by intro-ducing the RRGMRES algorithm,its numerical solution is gotten.Compared with the GMRES algorithm,the numerical simulation results show that the RRGM-RES algorithm has the advantages of high precision and strong anti-interference in solving such problems.

关 键 词：FREDHOLM 积分方程 二维 数值积分 不适定问题 RRGMRES算法 

分 类 号：O241.8[理学—计算数学]