QUADRATURE METHOD FOR SINGULAR INTEGRAL-EQUATIONS ON CLOSED CURVES

A method which combines quadrature with trigonometric interpolation is proposed for singular integral equations on closed curves. For the case of the circle, the present method is shown to be equivalent to the trigonometric epsilon-collocation method together with numerical quadrature for the compact term, and is shown to be stable in L2 provided the operator A is invertible in L2. The results are extended to arbitrary C(infinity) curves, to give a complete error analysis in the scale of Sobolev spaces H(s). In the final section the case of a non-invertible operator A is considered.