Full collocation methods for some boundary integral equations |
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Authors: | Ricardo Celorrio Francisco-Javier Sayas |
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Affiliation: | (1) Departamento de Matemática Aplicada – EUITIZ, Universidad de Zaragoza, Corona de Aragón, E-50009 Zaragoza, Spain E-mail:;(2) Departamento de Matemática Aplicada – CPS, Universidad de Zaragoza, María de Luna, 3, E-50015 Zaragoza, Spain E-mail: |
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Abstract: | In this paper we propose a fully discretized version of the collocation method applied to integral equations of the first kind with logarithmic kernel. After a stability and convergence analysis is given, we prove the existence of an asymptotic expansion of the error, which justifies the use of Richardson extrapolation. We further show how these expansions can be translated to a new expansion of potentials calculated with the numerical solution of a boundary integral equation such as those treated before. Some numerical experiments, confirming our theoretical results, are given. This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | logarithmic integral equations collocation full discretization extrapolation 65R20 45L10 |
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