We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A Nyström Method for 2D Linear Fredholm Integral Equations on Curvilinear Domains.
- Authors
Laguardia, Anna Lucia; Russo, Maria Grazia
- Abstract
This paper is devoted to the numerical treatment of two-dimensional Fredholm integral equations, defined on general curvilinear domains of the plane. A Nyström method, based on a suitable Gauss-like cubature formula, recently proposed in the literature is proposed. The convergence, stability and good conditioning of the method are proved in suitable subspaces of continuous functions of Sobolev type. The cubature formula, on which the Nyström method is constructed, has an error that behaves like the best polynomial approximation of the integrand function. Consequently, it is also shown how the Nyström method inherits this property and, hence, the proposed numerical strategy is fast when the involved known functions are smooth. Some numerical examples illustrate the efficiency of the method, also in comparison with other methods known in the literature.
- Subjects
FREDHOLM equations; LINE integrals; CUBATURE formulas; SMOOTHNESS of functions; CONTINUOUS functions
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 23, p4859
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11234859