Error Analysis of Discrete Legendre Multi-Projection Methods for Nonlinear Fredholm Integral Equations. (4th May 2017)

• Record Type: Journal Article
• Authors: Das, Payel; Nelakanti, Gnaneshwar
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 5(2017)
• Page Start: 549
• Page End: 574
• Publication Date: 2017-05-04
• Subjects: Legendre polynomials -- multi-projection methods -- smooth kernel -- urysohn integral equations; 45B05 -- 45G10 -- 65R20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1248563
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, polynomially-based discrete M-Galerkin and M-collocation methods are proposed to solve nonlinear Fredholm integral equation with a smooth kernel. Using sufficiently accurate numerical quadrature rule, we establish superconvergence results for the approximate and iterated approximate solutions of discrete Legendre M-Galerkin and M-collocation methods in both infinity and L 2 -norm. Numerical examples are presented to illustrate the theoretical results.