Midpoint collocation for Cauchy singular integral equations |
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Authors: | G A Chandler |
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Institution: | (1) Department of Mathematics, University of Queensland, 4072 St. Lucia, Queensland, Australia |
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Abstract: | Summary A Cauchy singular integral equation on a smooth closed curve may be solved numerically using continuous piecewise linear functions and collocation at the midpoints of the underlying grid. Even if the grid is non-uniform, suboptimal rates of convergence are proved using a discrete maximum principle for a modified form of the collocation equations. The same techniques prove negative norm estimates when midpoint collocation is used to determine piecewise constant approximations to the solution of first kind equations with the logarithmic potential.This work was supported by the Australian Research Council through the program grant Numerical analysis for integrals, integral equations and boundary value problems![rdquo](/content/n4q72628h4181628/xxlarge8221.gif) |
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Keywords: | 65R20 45L10 |
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