A Chebyshev collocation method for solving Symm's integral equation for conformal mapping: a partial error analysis

A boundary integral representation for the conformal mappingfrom a simply connected domain onto a given canonical regionis presented. The conformal map can be constructed via the solutionof a first-kind integral equation with logarithmic kernel: Symm'sintegral equation. A novel method for solving this equationis presented and a partial error analysis, including convergencerates, is given. The analysis is also relevant to the solutionof Symm's equation on a smooth, open contour. A superconvergenceresult for the conformal mapping is proved. Now in the Department of Mathematics and Computer Science, Universtyof Leicester, Leicester LE1 7RH, UK.