Richardson Extrapolation of Superconvergent Projection-Type Methods for Hammerstein Equations*. (18th May 2020)

• Record Type: Journal Article
• Authors: Allouch, C.; Sbibih, D.; Tahrichi, M.
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 7(2020)
• Page Start: 806
• Page End: 821
• Publication Date: 2020-05-18
• Subjects: Hammerstein equation -- extrapolation -- interpolatory projection -- orthogonal projection -- superconvergence; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1704779
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: For a nonlinear Hammerstein equation with a smooth kernel, a method proposed recently, based on projection onto a space of piecewise polynomials of degree ≤ r − 1, is shown to have convergence of order 4 r . This paper shows that this method have asymptotic series expansion and the order of convergence can be further improved to 4 r + 2 by one step of Richardson extrapolation, assuming the calculation to be repeated with each subinterval halved. Some numerical results are given to illustrate this improvement.