SUPERCONVERGENT NYSTRÖM AND DEGENERATE KERNEL METHODS FOR INTEGRAL EQUATIONS OF THE SECOND KIND

We propose, in this paper, new methods for approximating the solution of a second kind integral equation with a smooth kernel or kernel having a discontinuity along the diagonal. By using an interpolatory projection at Gaussian points onto the space of (discontinuous) piecewise polynomials of degree ≤ r – 1, we prove that the proposed methods exhibit convergence orders 3r and 4r for the iterated version. In comparison with Kulkarni's of the same convergence order, we show that our methods are faster and simpler to implement. The theoretical results obtained are illustrated by some numerical examples.