Modified projection and the iterated modified projection methods for nonlinear integral equations

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Grammont, L (Author) Other; Kulkarni, RP (Author) Other; vasconcelos, pb (Author) FEP

Journal

Title: Journal of Integral Equations and Applications

Vol. 25

Pages: 481-516

ISSN: 0897-3962

Publisher: Rocky Mountain Mathematics Consortium

Indexing

ISI Web of Knowledge - 21 Citations

Scopus - 25 Citations

Other information

Authenticus ID: P-00G-00G

DOI: 10.1216/jie-2013-25-4-481

Abstract (EN): Consider a nonlinear operator equation x - K(x) = f, where K is a Urysohn integral operator with a smooth kernel. Using the orthogonal projection onto a space of discontinuous piecewise polynomials of degree <= r, previous authors have established an order r + 1 convergence for the Galerkin solution and 2r + 2 for the iterated Galerkin solution. Equivalent results have also been established for the interpolatory projection at Gauss points. In this paper, a modified projection method is shown to have convergence of order 3r + 3 and one step of iteration is shown to improve the order of convergence to 4r + 4. The size of the system of equations that must be solved, in implementing this method, remains the same as for the Galerkin method.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 36