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A numerical study of iterative refinement schemes for weakly singular integral equations

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Publication Date
Volume
18
Issue
5
Identifiers
DOI: 10.1016/j.aml.2004.03.020
Keywords
  • Weakly Singular Kernel
  • Fredholm Integral Equation
  • Projection Approximation
  • Iterative Refinement
  • Preconditioned Gmres
Disciplines
  • Computer Science

Abstract

Abstract Three iterative refinement schemes are studied for approximating the solutions of linear weakly singular Fredholm integral equations of the second kind. The rates of convergence and computational costs of the three schemes are studied and compared with the classical approach by applying them respectively to: (i) a sparse linear system associated with an integral equation modelling a real life Astrophysics problem, and (ii) an integral equation whose associated linear problem is dense.

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