Projection methods based on grids for weakly singular integral equations
| Autor: | Filomena D. d' Almeida, Rosário Fernandes |
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| Přispěvatelé: | Universidade do Minho, Faculdade de Engenharia |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Matemática
Matemática Discretization Banach space 010103 numerical & computational mathematics Fredholm integral equation 01 natural sciences Projection (linear algebra) symbols.namesake Iterative refinement Applied mathematics Weakly singular integral operators 0101 mathematics Mathematics Ciências Naturais::Matemáticas Matemática [Ciências exactas e naturais] Numerical Analysis Science & Technology Basis (linear algebra) Applied Mathematics Mathematical analysis Mathematics [Natural sciences] Singular integral 010101 applied mathematics Computational Mathematics Error bounds Projection approximations in L1 symbols Mathematics Mathematics Subspace topology Matemáticas [Ciências Naturais] |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | For the solution of a weakly singular Fredholm integral equation of the 2nd kind defined on a Banach space, for instance L^1([a,b]), the classical projection methods with the discretization of the approximating operator on a finite dimensional subspace usually use a basis of this subspace built with grids on [a,b]. This may require a large dimension of the subspace. One way to overcome this problem is to include more information in the approximating operator or to compose one classical method with one step o iterative refinement. This is the case of Kulkarni method or iterated Kantorovich method. Here we compare these methods in terms of accuracy and arithmetic workload. A theorem stating comparable error bounds for these methods, under very weak assumptions on the kernel, the solution and the space where the problem is set, is given. The authors warmly thank Mario Paul Ahues Blanchait for his collaboration in this work by useful remarks, suggestions and ideas. The first author was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020. info:eu-repo/semantics/publishedVersion |
| Databáze: | OpenAIRE |
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