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求解非定常Lavrentiev迭代方程的多尺度配置法

罗兴钧, 江伟娟, 张荣   

  1. 赣南师范大学数学与计算机科学学院, 赣州 341000
  • 收稿日期:2021-07-20 出版日期:2022-05-14 发布日期:2022-05-06
  • 基金资助:
    国家自然科学基金(11761010)资助.

罗兴钧, 江伟娟, 张荣. 求解非定常Lavrentiev迭代方程的多尺度配置法[J]. 计算数学, 2022, 44(2): 257-271.

Luo Xingjun, Jiang Weijuan, Zhang Rong. MULTI-SCALE COLLOCATION METHOD FOR SOLVING NONSTATIONARY LAVRENTIEV ITERATIVE EQUATIONS[J]. Mathematica Numerica Sinica, 2022, 44(2): 257-271.

MULTI-SCALE COLLOCATION METHOD FOR SOLVING NONSTATIONARY LAVRENTIEV ITERATIVE EQUATIONS

Luo Xingjun, Jiang Weijuan, Zhang Rong   

  1. College of Mathematics and Computer science, Gannan Normal University, Ganzhou 341000, China
  • Received:2021-07-20 Online:2022-05-14 Published:2022-05-06
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.

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