A numerical method for two-dimensional Hammerstein integral equations
DOI:
https://doi.org/10.24193/subbmath.2021.2.03Keywords:
Hammerstein integral equations, spline collocation, interpolationAbstract
In this paper we investigate a collocation method for the approximate solution of Hammerstein integral equations in two dimensions. We start with a special type of piecewise linear interpolation over triangles for a reformulation of the equation. This leads to a numerical integration scheme that can then be extended to a domain in $\r^2$, which is used in collocation. We analyze and prove the convergence of the method and give error estimates. Because the quadrature formula has a higher degree of precision than expected with linear interpolation, the resulting collocation method is superconvergent at the nodes. We show the applicability of the proposed scheme on a numerical example and discuss future research ideas in this area.Downloads
Published
2021-06-15
Issue
Section
Articles
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
