The Galerkin method for singular integral equations revisited (Q1196846)

The author studies the approximate solution of the Cauchy singular integral equation with constant coefficients on the interval \((-1,1)\), using Galerkin's method based on orthogonal polynomials with respect to the usual Jacobi weight. He develops his earlier work [BIT 25, 413-419 (1985; Zbl 0607.65086)], showing that the error bounds in the uniform norm are sharp. Moreover, a class of right-hand sides is discussed where the Galerkin method may lead to unsatisfactory numerical results.