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Volume 41, Issue 6
A Multiscale Projection Method for Solving Nonlinear Integral Equations Under the Lipschitz Condition

Linxiu Fan, Xingjun Luo, Rong Zhang, Chunmei Zeng & Suhua Yang

DOI: 10.4208/jcm.2202-m2021-0206

J. Comp. Math., 41 (2023), pp. 1222-1245.

Published online: 2023-11

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  • Abstract

We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations. An a posteriori rule is suggested to choose the stopping index of iteration and the rates of convergence are also derived under the Lipschitz condition. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.

  • Keywords

Nonlinear integral equations, Multiscale Galerkin method, parameter choice strategy, Gauss-Newton method.

  • AMS Subject Headings

65J20, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-41-1222, author = {Fan , LinxiuLuo , XingjunZhang , RongZeng , Chunmei and Yang , Suhua}, title = {A Multiscale Projection Method for Solving Nonlinear Integral Equations Under the Lipschitz Condition}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {6}, pages = {1222--1245}, abstract = {

We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations. An a posteriori rule is suggested to choose the stopping index of iteration and the rates of convergence are also derived under the Lipschitz condition. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2202-m2021-0206}, url = {http://global-sci.org/intro/article_detail/jcm/22110.html} }
TY - JOUR T1 - A Multiscale Projection Method for Solving Nonlinear Integral Equations Under the Lipschitz Condition AU - Fan , Linxiu AU - Luo , Xingjun AU - Zhang , Rong AU - Zeng , Chunmei AU - Yang , Suhua JO - Journal of Computational Mathematics VL - 6 SP - 1222 EP - 1245 PY - 2023 DA - 2023/11 SN - 41 DO - http://doi.org/10.4208/jcm.2202-m2021-0206 UR - https://global-sci.org/intro/article_detail/jcm/22110.html KW - Nonlinear integral equations, Multiscale Galerkin method, parameter choice strategy, Gauss-Newton method. AB -

We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations. An a posteriori rule is suggested to choose the stopping index of iteration and the rates of convergence are also derived under the Lipschitz condition. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.

Fan , LinxiuLuo , XingjunZhang , RongZeng , Chunmei and Yang , Suhua. (2023). A Multiscale Projection Method for Solving Nonlinear Integral Equations Under the Lipschitz Condition. Journal of Computational Mathematics. 41 (6). 1222-1245. doi:10.4208/jcm.2202-m2021-0206
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