Midpoint collocation for Cauchy singular integral equations
The author studies the numerical solution of a Cauchy singular integral equation of the first kind on a smooth closed curve, using continuous piecewise linear functions and collocation at the midpoints of the underlying grid. He presents an interesting and new approach to the convergence analysis of this method, only assuming that the local mesh ratio is bounded. Suboptimal rates of convergence are proved using a discrete maximum principle for a modified form of the collocation equations. The results are extended to the case of piecewise constant midpoint collocation for the logarithmic potential operator.
Cauchy singular integral equation of the first kind
scientific article; zbMATH DE number 118309
scientific article