2-GRID SOLUTION OF SYMM INTEGRAL-EQUATION

We propose two-grid iteration methods for Symm's integral equation dis cretized by quadrature-collocation or quadrature methods. Asymptotical ly the optimal order of error estimate is achieved already on the firs t iteration, for some modifications on the second iteration. This enab les us to introduce some solvers which are of the optimal convergence order and cheap in a practical implementation; the cost varies between O(N-2) and O(N log N) arithmetic operations. Numerical experiments co nfirm the approximation properties of the schemes.