A modified iterated projection method adapted to a nonlinear integral equation

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Grammont, L (Author) Other; Vasconcelos, PB (Author) FEP; Ahues, M (Author) Other

Journal

Title: Applied Mathematics and Computation

Vol. 276

Pages: 432-441

ISSN: 0096-3003

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 13 Citations

Scopus - 14 Citations

Other information

Authenticus ID: P-00K-23Y

DOI: 10.1016/j.amc.2015.12.019

Abstract (EN): The classical way to tackle a nonlinear Fredholm integral equation of the second kind is to adapt the discretization scheme from the linear case. The Iterated projection method is a popular method since it shows, in most cases, superconvergence and it is easy to implement. The problem is that the accuracy of the approximation is limited by the mesh size discretization. Better approximations can only be achieved for fine discretizations and the size of the linear system to be solved then becomes very large: its dimension grows up with an order proportional to the square of the mesh size. In order to overcome this difficulty, we propose a novel approach to first linearize the nonlinear equation by a Newton -type method and only then to apply the Iterated projection method to each of the linear equations issued from the Newton method. We prove that, for any value (large enough) of the discretization parameter, the approximation tends to the exact solution when the number of Newton iterations tends to infinity, so that we can attain any desired accuracy. Numerical experiments confirm this theoretical result. (C) 2016 Published by Elsevier Inc.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10