求解非定常Lavrentiev迭代方程的多尺度配置法  

MULTI-SCALE COLLOCATION METHOD FOR SOLVING NONSTATIONARY LAVRENTIEV ITERATIVE EQUATIONS

作　　者：罗兴钧[1] 江伟娟 张荣[1] Luo Xingjun;Jiang Weijuan;Zhang Rong(College of Mathematics and Computer science,Gannan Normal University,Ganzhou 341000,China)

机构地区：[1]赣南师范大学数学与计算机科学学院,赣州341000

出　　处：《计算数学》2022年第2期257-271,共15页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11761010)资助.

摘　　要：本文采用多尺度配置法求解第一类弱扇形积分方程.将压缩配置法用于投影离散非定常迭代正则化方程,得到了近似解在Banach空间范数下误差估计,给出了迭代停止准则,确保近似解无穷范数下的最优收敛率.优点是确保了收敛率,减少了计算量.数值例子验证了算法的有效性.In this paper,the multi-scale collocation method is used to solve the first type of weak sector integral equation.The compressed configuration method is used to project the discrete nonstationary iterative regularization equation,and the error estimate of the approximate solution under the Banach space norm is obtained,and the iteration stopping criterion is given to ensure the optimal convergence rate of the approximate solution under the infinite norm.The advantage is to ensure the convergence rate and reduce the amount of calculation.Numerical examples verify the effectiveness of the algorithm.

关 键 词：非定常迭代 多尺度配置法 平衡准则 最优收敛率 

分 类 号：O241.6[理学—计算数学]