A Modified Minimal Error Method for Solving Nonlinear Integral Equations via Multiscale Galerkin Methods. (2nd January 2022)

• Record Type: Journal Article
• Authors: Yang, Hongqi; Zhang, Rong
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 1(2022)
• Page Start: 1
• Page End: 15
• Publication Date: 2022-01-02
• Subjects: Modified minimal error method -- multiscale Galerkin methods -- nonlinear integral equations -- the discrepancy principle; 65J20 -- 65D25 -- 47A52 -- 47J06; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1968899
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: A modified minimal error method for nonlinear integral equations is established. Such method, combined with the discrepancy principle as stopping rule, is a regularization method, which yields convergence to an exact solution when the nonlinear operator F satisfies certain conditions. Furthermore, the convergence of the modified minimal error method via multiscale Galerkin methods is also proved. Finally, numerical results show the accuracy and efficiency of the proposed method.