Cosine Change of Variable for Symm's Integral Equation on Open Arcs

By applying a cosine change of variable, the numerical solutionof Symm's integral equation on open arcs can be obtained inan effective way so that the influence of the singularitiesat the endpoints is eliminated. Both Galerkin and collocationmethods using a piecewise constant approximating space are analysed.The convergence of the approximate solutions and the superconvergenceof the single layer potential as well as some numerical resultsare presented.