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

• Tipo: Artigo em Revista Científica Internacional
• Data: 2013

Autores

Grammont, L (Autor) Outra; Kulkarni, RP (Autor) Outra; vasconcelos, pb (Autor) FEP

Revista

Título: Journal of Integral Equations and Applications

Vol. 25

Páginas: 481-516

ISSN: 0897-3962

Editora: Rocky Mountain Mathematics Consortium

Indexação

ISI Web of Knowledge - 21 Citações

Scopus - 25 Citações

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 36