Two Singularity Subtraction Schemes for a Class of Nonlinear Weakly Singular Integral Equations. (4th July 2022)

• Record Type: Journal Article
• Authors: Ahues, M.; Dias d'Almeida, F.; Fernandes, R.; Vasconcelos, P. B.
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 9(2022)
• Page Start: 1114
• Page End: 1139
• Publication Date: 2022-07-04
• Subjects: Approximation theory -- convergence analysis -- nonlinear analysis -- numerical methods; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2088790
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Singularity subtraction for linear weakly singular Fredholm integral equations of the second kind is generalized to nonlinear integral equations. Two approaches are presented: The Classical Approach discretizes the nonlinear problem, and uses some finite dimensional linearization process to solve numerically the discrete problem. Its convergence is proved under mild hypotheses on the nonlinearity and the quadrature rule of the singularity subtraction scheme. The New Approach is based on linearization of the problem in its infinite dimensional setting, and discretization of the sequence of linear problems by singularity subtraction. It is more efficient than the former, as three numerical experiments confirm.