The numerical solution of first-kind logarithmic-kernel integral equations on smooth open arcs

Authors:
Kendall E. Atkinson and Ian H. Sloan

Journal:
Math. Comp. **56** (1991), 119-139

MSC:
Primary 65R20; Secondary 31A10, 35C15

DOI:
https://doi.org/10.1090/S0025-5718-1991-1052084-0

MathSciNet review:
1052084

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider solving the Dirichlet problem

*S*a smooth

*open*curve in the plane. We use single-layer potentials to construct a solution . This leads to the solution of equations of the form

*principal part*, which is explicitly invertible, and a compact perturbation. Then a

*discrete Galerkin method*that takes special advantage of the splitting of the integral equation is used to solve the equation numerically. A complete convergence analysis is given; numerical examples conclude the paper.

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DOI:
https://doi.org/10.1090/S0025-5718-1991-1052084-0

Article copyright:
© Copyright 1991
American Mathematical Society